diff --git a/include/reduced_basis/rb_parameters.h b/include/reduced_basis/rb_parameters.h
index 778e49d5d79..2f95fd19e52 100644
--- a/include/reduced_basis/rb_parameters.h
+++ b/include/reduced_basis/rb_parameters.h
@@ -44,11 +44,17 @@ class RBParameters
 {
 public:
 
+  /**
+   * Constructor. Initializes the _n_steps parameter to 1 for
+   * backwards compatibility, but the set_n_steps() function can
+   * always be called later to update this value.
+   */
+  RBParameters();
+
   /**
    * The special functions can be defaulted for this class, as it
    * does not manage any memory itself.
    */
-  RBParameters () = default;
   RBParameters (RBParameters &&) = default;
   RBParameters (const RBParameters &) = default;
   RBParameters & operator= (const RBParameters &) = default;
@@ -257,6 +263,16 @@ class RBParameters
    */
   unsigned int n_parameters() const;
 
+  /**
+   * Set the number of steps this RBParameters object is intended to
+   * represent, in the case that there are no actual parameters stored
+   * on it. Note: this value will only be used in the no-parameters
+   * case; if there are actual parameters specified in this class, the
+   * number set via this API is ignored. All parameters stored within
+   * the RBParameters object must have n_steps() steps.
+   */
+  void set_n_steps(unsigned int n_steps);
+
   /**
    * Returns the number of steps stored for all parameters. For
    * simplicity, we require all parameters to store the same number of
@@ -352,6 +368,14 @@ class RBParameters
                         std::size_t index,
                         Real value);
 
+  /**
+   * The number of steps represented by this RBParameters object, in
+   * the case where there are no parameters actually stored on it. If
+   * there are parameters stored on this RBParameters object, then the
+   * n_steps() API returns that number of steps instead.
+   */
+  unsigned int _n_steps;
+
   /**
    * The map that stores the actual parameter vectors. Each vector is
    * indexed by a name.
diff --git a/src/reduced_basis/rb_parameters.C b/src/reduced_basis/rb_parameters.C
index a58c7aa830c..ce3345ff6ed 100644
--- a/src/reduced_basis/rb_parameters.C
+++ b/src/reduced_basis/rb_parameters.C
@@ -27,6 +27,11 @@
 namespace libMesh
 {
 
+RBParameters::RBParameters() :
+  _n_steps(1)
+{
+}
+
 RBParameters::RBParameters(const std::map<std::string, Real> & parameter_map)
 {
   // Backwards compatible support for constructing an RBParameters
@@ -38,6 +43,7 @@ RBParameters::RBParameters(const std::map<std::string, Real> & parameter_map)
 
 void RBParameters::clear()
 {
+  _n_steps = 1;
   _parameters.clear();
   _extra_parameters.clear();
 }
@@ -159,11 +165,16 @@ unsigned int RBParameters::n_parameters() const
   return cast_int<unsigned int>(_parameters.size());
 }
 
+void RBParameters::set_n_steps(unsigned int n_steps)
+{
+  _n_steps = n_steps;
+}
+
 unsigned int RBParameters::n_steps() const
 {
   // Quick return if there are no parameters
   if (_parameters.empty())
-    return 0;
+    return _n_steps;
 
   // If _parameters is not empty, we can check the number of steps in the first param
   auto size_first = _parameters.begin()->second.size();
diff --git a/src/reduced_basis/rb_theta.C b/src/reduced_basis/rb_theta.C
index 02e69c37bd1..09aaedfd805 100644
--- a/src/reduced_basis/rb_theta.C
+++ b/src/reduced_basis/rb_theta.C
@@ -25,14 +25,37 @@
 namespace libMesh
 {
 
-Number RBTheta::evaluate(const RBParameters &) { return 1.; }
+Number RBTheta::evaluate(const RBParameters & mu)
+{
+  // The RBTheta::evaluate() API is not general enough to handle the
+  // multi-step RBParameters case, and you must therefore call
+  // RBTheta::evaluate_vec() instead.
+  libmesh_error_msg_if(mu.n_steps() > 1,
+                       "You should only call the evaluate_vec() API when using multi-step RBParameters objects.");
+
+  return 1.;
+}
 
 std::vector<Number>
 RBTheta::evaluate_vec(const std::vector<RBParameters> & mus)
 {
-  std::vector<Number> result(mus.size());
-  for (auto i : index_range(mus))
-    result[i] = evaluate(mus[i]);
+  // Eventual return value
+  std::vector<Number> result;
+
+  for (const auto & mu : mus)
+    {
+      // Backwards-compatible behavior: for single-step RBParameters objects, we fall back on
+      // calling the scalar evaluate() function for this RBTheta object, which may have been
+      // overridden by the user.
+      if (mu.n_steps() == 1)
+        result.push_back( this->evaluate(mu) );
+      else
+        {
+          // For multistep RBParameters objects, all we can do is return
+          // mu.n_steps() copies of 1 here at the base class level.
+          result.insert(result.end(), /*count=*/mu.n_steps(), /*val=*/1.);
+        }
+    }
 
   return result;
 }
diff --git a/tests/utils/rb_parameters_test.C b/tests/utils/rb_parameters_test.C
index 73b3041e9cf..275185f9380 100644
--- a/tests/utils/rb_parameters_test.C
+++ b/tests/utils/rb_parameters_test.C
@@ -14,6 +14,7 @@ public:
   CPPUNIT_TEST( testOldConstructor );
   CPPUNIT_TEST( testIterators );
   CPPUNIT_TEST( testAppend );
+  CPPUNIT_TEST( testNSteps );
   CPPUNIT_TEST_SUITE_END();
 
 public:
@@ -117,6 +118,25 @@ public:
     for (int i=0; i<3; ++i)
       CPPUNIT_ASSERT_EQUAL(params1.get_step_value("b", i), Real(i+3));
   }
+
+  void testNSteps()
+  {
+    LOG_UNIT_TEST;
+
+    // A default-constructed RBparameters object has 1 step by definition
+    RBParameters params;
+    CPPUNIT_ASSERT_EQUAL(params.n_steps(), static_cast<unsigned int>(1));
+
+    // Set the number of steps to use in the no-parameters case
+    params.set_n_steps(10);
+    CPPUNIT_ASSERT_EQUAL(params.n_steps(), static_cast<unsigned int>(10));
+
+    // Define multiple steps for a single parameter. Now we no longer
+    // use the set_n_steps() value, since we have actual steps.
+    params.push_back_value("a", 1.);
+    params.push_back_value("a", 2.);
+    CPPUNIT_ASSERT_EQUAL(params.n_steps(), static_cast<unsigned int>(2));
+  }
 };
 
 CPPUNIT_TEST_SUITE_REGISTRATION ( RBParametersTest );