diff --git a/src/Test/Test.jl b/src/Test/Test.jl
index b4ff5aaa37..f774a6203a 100644
--- a/src/Test/Test.jl
+++ b/src/Test/Test.jl
@@ -12,6 +12,7 @@ mutable struct Config{T<:Real}
     atol::T
     rtol::T
     optimal_status::MOI.TerminationStatusCode
+    infeasible_status::MOI.TerminationStatusCode
     exclude::Vector{Any}
 end
 
@@ -21,6 +22,7 @@ end
         atol::Real = Base.rtoldefault(T),
         rtol::Real = Base.rtoldefault(T),
         optimal_status::MOI.TerminationStatusCode = MOI.OPTIMAL,
+        infeasible_status::MOI.TerminationStatusCode = MOI.INFEASIBLE,
         exclude::Vector{Any} = Any[],
     ) where {T}
 
@@ -34,6 +36,8 @@ Return an object that is used to configure various tests.
     when comparing solutions.
   * `optimal_status = MOI.OPTIMAL`: Set to `MOI.LOCALLY_SOLVED` if the solver
     cannot prove global optimality.
+  * `infeasible_status = MOI.INFEASIBLE`: Set to `MOI.LOCALLY_INFEASIBLE` if the
+    solver cannot prove global infeasibility.
   * `exclude = Vector{Any}`: Pass attributes or functions to `exclude` to skip
     parts of tests that require certain functionality. Common arguments include:
      - `MOI.delete` to skip deletion-related tests
@@ -64,9 +68,10 @@ function Config(
     atol::Real = Base.rtoldefault(T),
     rtol::Real = Base.rtoldefault(T),
     optimal_status::MOI.TerminationStatusCode = MOI.OPTIMAL,
+    infeasible_status::MOI.TerminationStatusCode = MOI.INFEASIBLE,
     exclude::Vector{Any} = Any[],
 ) where {T<:Real}
-    return Config{T}(atol, rtol, optimal_status, exclude)
+    return Config{T}(atol, rtol, optimal_status, infeasible_status, exclude)
 end
 
 function Base.copy(config::Config{T}) where {T}
@@ -74,6 +79,7 @@ function Base.copy(config::Config{T}) where {T}
         config.atol,
         config.rtol,
         config.optimal_status,
+        config.infeasible_status,
         copy(config.exclude),
     )
 end
diff --git a/src/Test/test_conic.jl b/src/Test/test_conic.jl
index fbd1a37f49..bed8b1d5ea 100644
--- a/src/Test/test_conic.jl
+++ b/src/Test/test_conic.jl
@@ -521,7 +521,7 @@ function test_conic_linear_INFEASIBLE(model::MOI.ModelLike, config::Config)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
         @test MOI.get(model, MOI.TerminationStatus()) in
-              [MOI.INFEASIBLE, MOI.INFEASIBLE_OR_UNBOUNDED]
+              [config.infeasible_status, MOI.INFEASIBLE_OR_UNBOUNDED]
         # TODO test dual feasibility and objective sign
     end
     return
@@ -597,7 +597,7 @@ function test_conic_linear_INFEASIBLE_2(model::MOI.ModelLike, config::Config)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
         @test MOI.get(model, MOI.TerminationStatus()) in
-              [MOI.INFEASIBLE, MOI.INFEASIBLE_OR_UNBOUNDED]
+              [config.infeasible_status, MOI.INFEASIBLE_OR_UNBOUNDED]
         # TODO test dual feasibility and objective sign
     end
     return
@@ -928,7 +928,8 @@ function test_conic_NormInfinityCone_INFEASIBLE(
     if _supports(config, MOI.optimize!)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+        @test MOI.get(model, MOI.TerminationStatus()) ==
+              config.infeasible_status
         @test MOI.get(model, MOI.PrimalStatus()) in
               (MOI.NO_SOLUTION, MOI.INFEASIBLE_POINT)
         # TODO test dual feasibility and objective sign
@@ -1351,7 +1352,8 @@ function test_conic_NormOneCone_INFEASIBLE(model::MOI.ModelLike, config::Config)
     if _supports(config, MOI.optimize!)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+        @test MOI.get(model, MOI.TerminationStatus()) ==
+              config.infeasible_status
         @test MOI.get(model, MOI.PrimalStatus()) in
               (MOI.NO_SOLUTION, MOI.INFEASIBLE_POINT)
         # TODO test dual feasibility and objective sign
@@ -2005,7 +2007,8 @@ function test_conic_SecondOrderCone_INFEASIBLE(
     if _supports(config, MOI.optimize!)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+        @test MOI.get(model, MOI.TerminationStatus()) ==
+              config.infeasible_status
         @test MOI.get(model, MOI.PrimalStatus()) in
               (MOI.NO_SOLUTION, MOI.INFEASIBLE_POINT)
         # TODO test dual feasibility and objective sign
@@ -2445,7 +2448,7 @@ function test_conic_RotatedSecondOrderCone_INFEASIBLE(
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
         @test MOI.get(model, MOI.TerminationStatus()) in
-              [MOI.INFEASIBLE, MOI.INFEASIBLE_OR_UNBOUNDED]
+              [config.infeasible_status, MOI.INFEASIBLE_OR_UNBOUNDED]
         has_certificate = MOI.get(model, MOI.DualStatus()) in [
             MOI.INFEASIBILITY_CERTIFICATE,
             MOI.NEARLY_INFEASIBILITY_CERTIFICATE,
diff --git a/src/Test/test_constraint.jl b/src/Test/test_constraint.jl
index 7b315a3933..57cca1aa75 100644
--- a/src/Test/test_constraint.jl
+++ b/src/Test/test_constraint.jl
@@ -609,7 +609,7 @@ function test_constraint_ZeroOne_bounds_3(model::MOI.ModelLike, config::Config)
     )
     x = MOI.get(model, MOI.VariableIndex, "x")
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     return
 end
 
diff --git a/src/Test/test_infeasibility_certificates.jl b/src/Test/test_infeasibility_certificates.jl
index 560dbb8c99..c9d20458ef 100644
--- a/src/Test/test_infeasibility_certificates.jl
+++ b/src/Test/test_infeasibility_certificates.jl
@@ -76,7 +76,8 @@ for sense in (MOI.MIN_SENSE, MOI.MAX_SENSE), offset in (0.0, 1.2)
             cu = MOI.add_constraint(model, 1.0 * x, MOI.LessThan(1.4))
             MOI.optimize!(model)
             @requires(
-                MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE,
+                MOI.get(model, MOI.TerminationStatus()) ==
+                config.infeasible_status,
             )
             @requires(
                 MOI.get(model, MOI.DualStatus()) ==
@@ -137,7 +138,8 @@ for sense in (MOI.MIN_SENSE, MOI.MAX_SENSE), offset in (0.0, 1.2)
             cu = MOI.add_constraint(model, x, MOI.LessThan(1.4))
             MOI.optimize!(model)
             @requires(
-                MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE,
+                MOI.get(model, MOI.TerminationStatus()) ==
+                config.infeasible_status,
             )
             @requires(
                 MOI.get(model, MOI.DualStatus()) ==
diff --git a/src/Test/test_linear.jl b/src/Test/test_linear.jl
index 8c3c9bd9c7..0610da3c05 100644
--- a/src/Test/test_linear.jl
+++ b/src/Test/test_linear.jl
@@ -1432,9 +1432,8 @@ function test_linear_INFEASIBLE(
     if _supports(config, MOI.optimize!)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE ||
-              MOI.get(model, MOI.TerminationStatus()) ==
-              MOI.INFEASIBLE_OR_UNBOUNDED
+        @test MOI.get(model, MOI.TerminationStatus()) in
+              (config.infeasible_status, MOI.INFEASIBLE_OR_UNBOUNDED)
         has_certificate =
             MOI.get(model, MOI.DualStatus()) == MOI.INFEASIBILITY_CERTIFICATE
         if _supports(config, MOI.ConstraintDual) && has_certificate
@@ -2334,9 +2333,8 @@ function test_linear_INFEASIBLE_2(
     if _supports(config, MOI.optimize!)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
         MOI.optimize!(model)
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE ||
-              MOI.get(model, MOI.TerminationStatus()) ==
-              MOI.INFEASIBLE_OR_UNBOUNDED
+        @test MOI.get(model, MOI.TerminationStatus()) in
+              (config.infeasible_status, MOI.INFEASIBLE_OR_UNBOUNDED)
         has_certificate =
             MOI.get(model, MOI.DualStatus()) == MOI.INFEASIBILITY_CERTIFICATE
         if _supports(config, MOI.ConstraintDual) && has_certificate
@@ -3982,9 +3980,8 @@ function _test_linear_SemiXXX_integration(
     MOI.set(model, MOI.ConstraintSet(), vc2, MOI.EqualTo(T(4)))
     if _supports(config, MOI.optimize!)
         MOI.optimize!(model)
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE ||
-              MOI.get(model, MOI.TerminationStatus()) ==
-              MOI.INFEASIBLE_OR_UNBOUNDED
+        @test MOI.get(model, MOI.TerminationStatus()) in
+              (config.infeasible_status, MOI.INFEASIBLE_OR_UNBOUNDED)
     end
     return
 end
diff --git a/src/Test/test_solve.jl b/src/Test/test_solve.jl
index 75f62ad2d6..fc39096c38 100644
--- a/src/Test/test_solve.jl
+++ b/src/Test/test_solve.jl
@@ -426,7 +426,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_EqualTo_upper(
         MOI.EqualTo(-1.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -481,7 +481,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_EqualTo_lower(
         MOI.EqualTo(1.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -535,7 +535,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_LessThan(
         MOI.LessThan(-1.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -590,7 +590,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_GreaterThan(
         MOI.GreaterThan(1.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -645,7 +645,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_Interval_upper(
         MOI.Interval(-2.0, -1.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -700,7 +700,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_Interval_lower(
         MOI.Interval(1.0, 2.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -755,7 +755,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_VariableIndex_LessThan(
         MOI.GreaterThan(1.0),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -814,7 +814,7 @@ function test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_VariableIndex_LessThan_
     MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
     MOI.set(model, MOI.ObjectiveFunction{MOI.VariableIndex}(), x[1])
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     if MOI.get(model, MOI.DualStatus()) != MOI.INFEASIBILITY_CERTIFICATE
         return
     end
@@ -910,7 +910,7 @@ function test_solve_conflict_bound_bound(
     @test MOI.get(model, MOI.ConflictStatus()) ==
           MOI.COMPUTE_CONFLICT_NOT_CALLED
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     @test MOI.get(model, MOI.ConstraintConflictStatus(), c1) == MOI.IN_CONFLICT
@@ -974,7 +974,7 @@ function test_solve_conflict_two_affine(
     @test MOI.get(model, MOI.ConflictStatus()) ==
           MOI.COMPUTE_CONFLICT_NOT_CALLED
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     @test MOI.get(model, MOI.ConstraintConflictStatus(), c1) == MOI.IN_CONFLICT
@@ -1033,7 +1033,7 @@ function test_solve_conflict_invalid_interval(
     @test MOI.get(model, MOI.ConflictStatus()) ==
           MOI.COMPUTE_CONFLICT_NOT_CALLED
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     @test MOI.get(model, MOI.ConstraintConflictStatus(), c1) == MOI.IN_CONFLICT
@@ -1095,7 +1095,7 @@ function test_solve_conflict_affine_affine(
     @test MOI.get(model, MOI.ConflictStatus()) ==
           MOI.COMPUTE_CONFLICT_NOT_CALLED
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     @test MOI.get(model, MOI.ConstraintConflictStatus(), b1) == MOI.IN_CONFLICT
@@ -1169,7 +1169,7 @@ function test_solve_conflict_EqualTo(
     @test MOI.get(model, MOI.ConflictStatus()) ==
           MOI.COMPUTE_CONFLICT_NOT_CALLED
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     @test MOI.get(model, MOI.ConstraintConflictStatus(), b1) == MOI.IN_CONFLICT
@@ -1243,7 +1243,7 @@ function test_solve_conflict_NOT_IN_CONFLICT(
     @test MOI.get(model, MOI.ConflictStatus()) ==
           MOI.COMPUTE_CONFLICT_NOT_CALLED
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     @test MOI.get(model, MOI.ConstraintConflictStatus(), b1) == MOI.IN_CONFLICT
@@ -1363,7 +1363,7 @@ function test_solve_conflict_zeroone(
         MOI.GreaterThan(T(2)),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     zeroone_conflict = MOI.get(model, MOI.ConstraintConflictStatus(), c1)
@@ -1426,7 +1426,7 @@ function test_solve_conflict_zeroone_2(
         MOI.EqualTo(one(T) / T(2)),
     )
     MOI.optimize!(model)
-    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
+    @test MOI.get(model, MOI.TerminationStatus()) == config.infeasible_status
     MOI.compute_conflict!(model)
     @test MOI.get(model, MOI.ConflictStatus()) == MOI.CONFLICT_FOUND
     zeroone_conflict = MOI.get(model, MOI.ConstraintConflictStatus(), c1)