diff --git a/include/reduced_basis/rb_parameters.h b/include/reduced_basis/rb_parameters.h
index 8048240c218..5410eeae0f2 100644
--- a/include/reduced_basis/rb_parameters.h
+++ b/include/reduced_basis/rb_parameters.h
@@ -198,14 +198,14 @@ class RBParameters
    * Get the value of the specified parameter at the specified step,
    * throwing an error if it does not exist.
    */
-  Real get_step_value(const std::string & param_name, std::size_t index) const;
+  Real get_step_value(const std::string & param_name, std::size_t step) const;
 
   /**
    * Get the value of the specified parameter at the specified step,
    * returning the provided default value if either the parameter is
    * not defined or the step is invalid.
    */
-  Real get_step_value(const std::string & param_name, std::size_t index, const Real & default_val) const;
+  Real get_step_value(const std::string & param_name, std::size_t step, const Real & default_val) const;
 
   /**
    * Set the value of the specified parameter. If param_name
@@ -232,6 +232,11 @@ class RBParameters
    */
   void push_back_value(const std::string & param_name, Real value);
 
+  /**
+   * Same as push_back_value(), but for "extra" parameters.
+   */
+  void push_back_extra_value(const std::string & param_name, Real value);
+
   /**
    * Get the value of the specified extra parameter, throwing an error
    * if it does not exist.
@@ -244,6 +249,19 @@ class RBParameters
    */
   Real get_extra_value(const std::string & param_name, const Real & default_val) const;
 
+  /**
+   * Get the value of the specified "extra" parameter at the specified step,
+   * throwing an error if it does not exist.
+   */
+  Real get_extra_step_value(const std::string & param_name, std::size_t step) const;
+
+  /**
+   * Get the value of the specified extra parameter at the specified step,
+   * returning the provided default value if either the parameter is
+   * not defined or the step is invalid.
+   */
+  Real get_extra_step_value(const std::string & param_name, std::size_t step, const Real & default_val) const;
+
   /**
    * Set the value of the specified extra parameter. If param_name
    * doesn't already exist, it is added to the extra parameters.
diff --git a/src/reduced_basis/rb_parameters.C b/src/reduced_basis/rb_parameters.C
index 1ee9f00bdee..23a1b1ade33 100644
--- a/src/reduced_basis/rb_parameters.C
+++ b/src/reduced_basis/rb_parameters.C
@@ -139,6 +139,13 @@ void RBParameters::push_back_value(const std::string & param_name, Real value)
   _parameters[param_name].push_back(value);
 }
 
+void RBParameters::push_back_extra_value(const std::string & param_name, Real value)
+{
+  // Get reference to vector of values for this extra parameter, creating it
+  // if it does not already exist, and push back the specified value.
+  _extra_parameters[param_name].push_back(value);
+}
+
 Real RBParameters::get_extra_value(const std::string & param_name) const
 {
   // Same as get_value(param_name) but for the map of extra parameters
@@ -154,6 +161,20 @@ Real RBParameters::get_extra_value(const std::string & param_name, const Real &
   return ((it != _extra_parameters.end() && it->second.size() != 0) ? it->second[0] : default_val);
 }
 
+Real RBParameters::get_extra_step_value(const std::string & param_name, std::size_t step) const
+{
+  const auto & vec = libmesh_map_find(_extra_parameters, param_name);
+  libmesh_error_msg_if(step >= vec.size(), "Error getting value for parameter " << param_name);
+  return vec[step];
+}
+
+Real RBParameters::get_extra_step_value(const std::string & param_name, std::size_t step, const Real & default_val) const
+{
+  // same as get_step_value(param_name, index, default_val) but for the map of extra parameters
+  auto it = _extra_parameters.find(param_name);
+  return ((it != _extra_parameters.end() && step < it->second.size()) ? it->second[step] : default_val);
+}
+
 void RBParameters::set_extra_value(const std::string & param_name, Real value)
 {
   // Same as set_value(param_name, value) but for the map of extra parameters
diff --git a/tests/utils/rb_parameters_test.C b/tests/utils/rb_parameters_test.C
index 275185f9380..c57d624bc54 100644
--- a/tests/utils/rb_parameters_test.C
+++ b/tests/utils/rb_parameters_test.C
@@ -105,7 +105,10 @@ public:
     // (must have same number of steps)
     RBParameters params2;
     for (int i=0; i<3; ++i)
-      params2.push_back_value("b", Real(i+3));
+      {
+        params2.push_back_value("b", Real(i+3));
+        params2.push_back_extra_value("c", Real(i*i));
+      }
 
     // Append second onto first
     params1 += params2;
@@ -115,8 +118,12 @@ public:
 
     // Check that the desired appending happened
     CPPUNIT_ASSERT(params1.has_value("b"));
+    CPPUNIT_ASSERT(params1.has_extra_value("c"));
     for (int i=0; i<3; ++i)
-      CPPUNIT_ASSERT_EQUAL(params1.get_step_value("b", i), Real(i+3));
+      {
+        CPPUNIT_ASSERT_EQUAL(params1.get_step_value("b", i), static_cast<Real>(i+3));
+        CPPUNIT_ASSERT_EQUAL(params1.get_extra_step_value("c", i), static_cast<Real>(i*i));
+      }
   }
 
   void testNSteps()