diff --git a/docs/src/submodules/FileFormats/overview.md b/docs/src/submodules/FileFormats/overview.md
index b7d77c4318..64a56a2c48 100644
--- a/docs/src/submodules/FileFormats/overview.md
+++ b/docs/src/submodules/FileFormats/overview.md
@@ -84,7 +84,7 @@ julia> print(read("file.mof.json", String))
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [
     {
diff --git a/src/FileFormats/MOF/MOF.jl b/src/FileFormats/MOF/MOF.jl
index 332cea9d67..0db934f969 100644
--- a/src/FileFormats/MOF/MOF.jl
+++ b/src/FileFormats/MOF/MOF.jl
@@ -7,7 +7,7 @@ import JSONSchema
 import MathOptInterface
 
 const MOI = MathOptInterface
-const SCHEMA_PATH = joinpath(@__DIR__, "mof.0.5.schema.json")
+const SCHEMA_PATH = joinpath(@__DIR__, "mof.0.6.schema.json")
 const VERSION = let data = JSON.parsefile(SCHEMA_PATH, use_mmap = false)
     VersionNumber(
         data["properties"]["version"]["properties"]["major"]["const"],
diff --git a/src/FileFormats/MOF/mof.0.5.schema.json b/src/FileFormats/MOF/mof.0.6.schema.json
similarity index 96%
rename from src/FileFormats/MOF/mof.0.5.schema.json
rename to src/FileFormats/MOF/mof.0.6.schema.json
index 42630b1deb..031e10ab37 100644
--- a/src/FileFormats/MOF/mof.0.5.schema.json
+++ b/src/FileFormats/MOF/mof.0.6.schema.json
@@ -1,6 +1,6 @@
 {
     "$schema": "https://json-schema.org/schema#",
-    "$id": "https://jump.dev/MathOptFormat/schemas/mof.0.5.schema.json",
+    "$id": "https://jump.dev/MathOptFormat/schemas/mof.0.6.schema.json",
     "title": "The schema for MathOptFormat",
     "type": "object",
     "required": ["version", "variables", "objective", "constraints"],
@@ -11,7 +11,7 @@
             "required": ["minor", "major"],
             "properties": {
                 "minor": {
-                    "const": 5
+                    "const": 6
                 },
                 "major": {
                     "const": 0
@@ -859,6 +859,19 @@
                         "minimum": 1
                     }
                 }
+            }, {
+                "description": "The set corresponding to a mixed complementarity constraint. Complementarity constraints should be specified with an AbstractVectorFunction-in-Complements(dimension) constraint. The dimension of the vector-valued function `F` must be `dimension`. This defines a complementarity constraint between the scalar function `F[i]` and the variable in `F[i + dimension/2]`. Thus, `F[i + dimension/2]` must be interpretable as a single variable `x_i` (e.g., `1.0 * x + 0.0`). The mixed complementarity problem consists of finding `x_i` in the interval `[lb, ub]` (i.e., in the set `Interval(lb, ub)`), such that the following holds: 1. `F_i(x) == 0` if `lb_i < x_i < ub_i`; 2. `F_i(x) >= 0` if `lb_i == x_i`; 3. `F_i(x) <= 0` if `x_i == ub_i`. Classically, the bounding set for `x_i` is `Interval(0, Inf)`, which recovers: `0 <= F_i(x) ⟂ x_i >= 0`, where the `⟂` operator implies `F_i(x) * x_i = 0`.",
+                "examples": ["{\"type\": \"Complements\", \"dimension\": 2}"],
+                "required": ["dimension"],
+                "properties": {
+                    "type": {
+                        "const": "Complements"
+                    },
+                    "dimension": {
+                        "type": "integer",
+                        "minimum": 2
+                    }
+                }
             }]
         }
     }
diff --git a/src/FileFormats/MOF/read.jl b/src/FileFormats/MOF/read.jl
index 1568ac58ca..0bbe4a7c50 100644
--- a/src/FileFormats/MOF/read.jl
+++ b/src/FileFormats/MOF/read.jl
@@ -316,6 +316,7 @@ end
     SOS1,
     SOS2,
     IndicatorSet,
+    Complements,
 )
 
 """
@@ -450,6 +451,10 @@ function set_to_moi(::Val{:DualExponentialCone}, ::Object)
     return MOI.DualExponentialCone()
 end
 
+function set_to_moi(::Val{:Complements}, object::Object)
+    return MOI.Complements(div(object["dimension"], 2))
+end
+
 # ========== Typed vector sets ==========
 
 function set_to_moi(::Val{:PowerCone}, object::Object)
diff --git a/src/FileFormats/MOF/write.jl b/src/FileFormats/MOF/write.jl
index f2417e48d1..2c3b893e53 100644
--- a/src/FileFormats/MOF/write.jl
+++ b/src/FileFormats/MOF/write.jl
@@ -302,3 +302,10 @@ function moi_to_object(
         "activate_on" => (I == MOI.ACTIVATE_ON_ONE) ? "one" : "zero",
     )
 end
+
+function moi_to_object(set::MOI.Complements, ::Dict{MOI.VariableIndex,String})
+    return OrderedObject(
+        "type" => "Complements",
+        "dimension" => MOI.dimension(set),
+    )
+end
diff --git a/test/FileFormats/MOF/MOF.jl b/test/FileFormats/MOF/MOF.jl
index ea55374620..072e284b70 100644
--- a/test/FileFormats/MOF/MOF.jl
+++ b/test/FileFormats/MOF/MOF.jl
@@ -388,6 +388,13 @@ end
             ["c1"],
         )
     end
+    @testset "Complements" begin
+        test_model_equality(
+            "variables: x, y\nc1: [x, y] in Complements(1)",
+            ["x", "y"],
+            ["c1"],
+        )
+    end
     @testset "vectoraffine-in-zeros" begin
         test_model_equality(
             """
diff --git a/test/FileFormats/MOF/empty_model.mof.json b/test/FileFormats/MOF/empty_model.mof.json
index 9ffe78963e..fd2bdbb2e4 100644
--- a/test/FileFormats/MOF/empty_model.mof.json
+++ b/test/FileFormats/MOF/empty_model.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [],
   "objective": {"sense": "feasibility"},
diff --git a/test/FileFormats/MOF/empty_model.mof.json.gz b/test/FileFormats/MOF/empty_model.mof.json.gz
deleted file mode 100644
index f5bd8e4089..0000000000
Binary files a/test/FileFormats/MOF/empty_model.mof.json.gz and /dev/null differ
diff --git a/test/FileFormats/MOF/failing_models/blank_variable_name.mof.json b/test/FileFormats/MOF/failing_models/blank_variable_name.mof.json
index 5db754148a..6087061742 100644
--- a/test/FileFormats/MOF/failing_models/blank_variable_name.mof.json
+++ b/test/FileFormats/MOF/failing_models/blank_variable_name.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [{"name": ""}],
   "objective": {
diff --git a/test/FileFormats/MOF/failing_models/missing_variable_name.mof.json b/test/FileFormats/MOF/failing_models/missing_variable_name.mof.json
index b31f23d407..109994f1ce 100644
--- a/test/FileFormats/MOF/failing_models/missing_variable_name.mof.json
+++ b/test/FileFormats/MOF/failing_models/missing_variable_name.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [{}],
   "objective": {
diff --git a/test/FileFormats/MOF/failing_models/unsupported_constraint_function.mof.json b/test/FileFormats/MOF/failing_models/unsupported_constraint_function.mof.json
index 1dea9c4210..339d4291c6 100644
--- a/test/FileFormats/MOF/failing_models/unsupported_constraint_function.mof.json
+++ b/test/FileFormats/MOF/failing_models/unsupported_constraint_function.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [{"name": "x"}],
   "objective": {
diff --git a/test/FileFormats/MOF/failing_models/unsupported_constraint_set.mof.json b/test/FileFormats/MOF/failing_models/unsupported_constraint_set.mof.json
index e7c05c577c..9d9ba2fc5a 100644
--- a/test/FileFormats/MOF/failing_models/unsupported_constraint_set.mof.json
+++ b/test/FileFormats/MOF/failing_models/unsupported_constraint_set.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [{"name": "x"}],
   "objective": {
diff --git a/test/FileFormats/MOF/failing_models/unsupported_objective_function.mof.json b/test/FileFormats/MOF/failing_models/unsupported_objective_function.mof.json
index b1c0806cf5..137e534849 100644
--- a/test/FileFormats/MOF/failing_models/unsupported_objective_function.mof.json
+++ b/test/FileFormats/MOF/failing_models/unsupported_objective_function.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [{"name": "x"}],
   "objective": {
diff --git a/test/FileFormats/MOF/failing_models/unsupported_objective_sense.mof.json b/test/FileFormats/MOF/failing_models/unsupported_objective_sense.mof.json
index 7307a3add7..7fca972376 100644
--- a/test/FileFormats/MOF/failing_models/unsupported_objective_sense.mof.json
+++ b/test/FileFormats/MOF/failing_models/unsupported_objective_sense.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [{"name": "x"}],
   "objective": {
diff --git a/test/FileFormats/MOF/nlp.mof.json b/test/FileFormats/MOF/nlp.mof.json
index 7e2633822e..0c7c6cbe5c 100644
--- a/test/FileFormats/MOF/nlp.mof.json
+++ b/test/FileFormats/MOF/nlp.mof.json
@@ -2,7 +2,7 @@
   "name": "MathOptFormat Model",
   "version": {
     "major": 0,
-    "minor": 5
+    "minor": 6
   },
   "variables": [
     {