diff --git a/CHANGES.current b/CHANGES.current
index 417bca656..d54db5ba8 100644
--- a/CHANGES.current
+++ b/CHANGES.current
@@ -7,6 +7,15 @@ the issue number to the end of the URL: https://github.com/swig/swig/issues/
 Version 4.2.0 (in progress)
 ===========================
 
+2022-12-02: wsfulton
+            #624 #1021 Improved template template parameters support. Previously, specifying more
+            than one simple template template parameter resulted in a parse error. Now
+            multiple template template parameters are working including instantiation with
+            %template. Example:
+
+              template <template<template<class> class, class> class Op, template<class> class X, class Y>
+              class C { ... };
+
 2022-11-29: bero
             Fix mismatch between #pragma GCC diagnostic push and pop statements
 
diff --git a/Examples/test-suite/common.mk b/Examples/test-suite/common.mk
index cd634081c..3a5e7f678 100644
--- a/Examples/test-suite/common.mk
+++ b/Examples/test-suite/common.mk
@@ -497,6 +497,7 @@ CPP_TEST_CASES += \
 	template_static \
 	template_tbase_template \
 	template_template_parameters \
+	template_template_template_parameters \
 	template_typedef \
 	template_typedef_class_template \
 	template_typedef_cplx \
diff --git a/Examples/test-suite/cpp11_type_aliasing.i b/Examples/test-suite/cpp11_type_aliasing.i
index ea4048408..8bef71247 100644
--- a/Examples/test-suite/cpp11_type_aliasing.i
+++ b/Examples/test-suite/cpp11_type_aliasing.i
@@ -112,3 +112,39 @@ using callback_t = int(*)(int);
 callback_t get_callback() { return mult2; }
 int call(callback_t funk, int param) { return funk(param); }
 %}
+
+
+// Template template parameters - from #1021
+%inline %{
+#include <type_traits>
+
+class Node {};
+struct AnyVal { typedef AnyVal Super; };
+
+template<template<typename D, typename O> class C, typename T, typename Super, typename Root, typename O>
+  using DeriveToBase = typename std::conditional<std::is_same<T, AnyVal>::value, Root, C<Super, O> >::type;
+
+template<class T, class Root, class RParent>
+  using ImmediateBase = typename std::conditional<std::is_same<T, AnyVal>::value, Root, RParent >::type;
+
+template<class D, typename _Super=AnyVal> class Expression {
+  typedef _Super Super;
+};
+
+void TestInstantiationsPart4() {
+  Expression<AnyVal, AnyVal::Super> express;
+  DeriveToBase<Expression, AnyVal, AnyVal, AnyVal, AnyVal> derive_to_base = AnyVal();
+}
+%}
+
+#if 0
+// TODO define and instantiate std::conditional and std::is_same
+%template(ExpressionInstantiation) Expression<AnyVal, AnyVal::Super>;
+%template(AnyTypeInstantiation) DeriveToBase<Expression, AnyVal, AnyVal, AnyVal, AnyVal>;
+
+%inline %{
+AnyVal takeAnyVal(DeriveToBase<Expression, AnyVal, AnyVal, AnyVal, AnyVal> av) {
+  return av;
+}
+%}
+#endif
diff --git a/Examples/test-suite/java/template_template_parameters_runme.java b/Examples/test-suite/java/template_template_parameters_runme.java
index 613f9087c..244e12985 100644
--- a/Examples/test-suite/java/template_template_parameters_runme.java
+++ b/Examples/test-suite/java/template_template_parameters_runme.java
@@ -14,7 +14,7 @@ public class template_template_parameters_runme {
   }
 
   public static void main(String argv[]) {
-    // Test first part
+    // Test part 1
     ListFastBool listBool = new ListFastBool();
     listBool.setItem(true);
     boolean x_boolean = listBool.getAllotype();
@@ -27,7 +27,7 @@ public class template_template_parameters_runme {
     if (listDouble.getItem() != 10.2)
       throw new RuntimeException("Failed");
 
-    // Test second part
+    // Test part 2
     FloatTestStruct floatTestStruct = new FloatTestStruct();
     FloatContainer2 floatContainer2 = floatTestStruct.getX();
     floatContainer2.setX(8.1f);
@@ -41,6 +41,10 @@ public class template_template_parameters_runme {
     IntTestStruct intTestStructReturned = template_template_parameters.TestStructContainer1Method(intTestStruct);
     if (intTestStructReturned.getX().getX() != 101)
       throw new RuntimeException("Failed");
+
+    // Test part 3
+    MyFootInt99 mfi99 = new MyFootInt99();
+    mfi99.OperatorPlusEquals(mfi99);
   }
 }
 
diff --git a/Examples/test-suite/java/template_template_template_parameters_runme.java b/Examples/test-suite/java/template_template_template_parameters_runme.java
new file mode 100644
index 000000000..519a9e068
--- /dev/null
+++ b/Examples/test-suite/java/template_template_template_parameters_runme.java
@@ -0,0 +1,36 @@
+
+
+import template_template_template_parameters.*;
+
+public class template_template_template_parameters_runme {
+
+  static {
+    try {
+	System.loadLibrary("template_template_template_parameters");
+    } catch (UnsatisfiedLinkError e) {
+      System.err.println("Native code library failed to load. See the chapter on Dynamic Linking Problems in the SWIG Java documentation for help.\n" + e);
+      System.exit(1);
+    }
+  }
+
+  public static void main(String argv[]) {
+    CustomAttrs custom_attrs = new CustomAttrs();
+    AC ac = new AC();
+    BAC bac = new BAC();
+    CBAC cbac = new CBAC();
+    DBAC dbac = new DBAC();
+
+    custom_attrs = ac.getAttributes();
+    custom_attrs = bac.getAttributes();
+    custom_attrs = cbac.getAttributes();
+    custom_attrs = dbac.getAttributes();
+
+    bac.BMethod(custom_attrs, ac);
+    cbac.BMethod(custom_attrs, ac);
+    dbac.BMethod(custom_attrs, ac);
+
+    cbac.CMethod(custom_attrs, bac);
+    dbac.DMethod(custom_attrs, bac);
+  }
+}
+
diff --git a/Examples/test-suite/python/template_template_parameters_runme.py b/Examples/test-suite/python/template_template_parameters_runme.py
index 4b0e27d9c..312935970 100644
--- a/Examples/test-suite/python/template_template_parameters_runme.py
+++ b/Examples/test-suite/python/template_template_parameters_runme.py
@@ -1,6 +1,6 @@
 from template_template_parameters import *
 
-# Test first part
+# Test part 1
 listBool = ListFastBool()
 listBool.item = True
 x_boolean = listBool.allotype
@@ -13,7 +13,7 @@ x_double = listDouble.allotype
 if listDouble.item != 10.2:
   raise RuntimeError("Failed")
 
-# Test second part
+# Test part 2
 floatTestStruct = FloatTestStruct()
 floatContainer2 = floatTestStruct.x
 floatContainer2.x = 8.1
@@ -28,3 +28,6 @@ intTestStructReturned = TestStructContainer1Method(intTestStruct)
 if intTestStructReturned.x.x != 101:
   raise RuntimeError("Failed")
 
+# Test part 3
+mfi99 = MyFootInt99()
+mfi99 += mfi99 # __iadd__
diff --git a/Examples/test-suite/template_template_parameters.i b/Examples/test-suite/template_template_parameters.i
index 53b18b0b0..68c26bebe 100644
--- a/Examples/test-suite/template_template_parameters.i
+++ b/Examples/test-suite/template_template_parameters.i
@@ -1,9 +1,8 @@
 %module template_template_parameters
 
-
 %inline %{
 
-/* part 1 */
+// part 1
 
   namespace pfc {
     template<typename t_item, template <typename> class t_alloc> class array_t {};
@@ -33,7 +32,7 @@ void TestInstantiations() {
   (void) myListImplInt;
 }
 
-/* part 2 */
+// part 2
 
 template<class T>
 struct Container1 { 
@@ -52,10 +51,10 @@ TestStruct<int, Container1> TestStructContainer1Method(TestStruct<int, Container
   ts1.x.x += 10;
   return ts1;
 }
-
 %}
 
-/* part 1 */
+
+// part 1
 %template(ListImplFastBool) list_impl_t<bool, pfc::array_t<bool, pfc::alloc_fast> >;
 %template(ListFastBool) list_tt<bool, pfc::alloc_fast>;
 
@@ -65,9 +64,31 @@ TestStruct<int, Container1> TestStructContainer1Method(TestStruct<int, Container
 %template(BoolAllocFast) pfc::alloc_fast<bool>;
 %template(DoubleAllocFast) pfc::alloc_fast<double>;
 
-/* part 2 */
+// part 2
 %template(IntContainer1) Container1<int>;
 %template(FloatContainer2) Container2<float>;
 %template(IntTestStruct) TestStruct<int, Container1>;
 %template(FloatTestStruct) TestStruct<float, Container2>;
 
+
+// part 3 - from #624
+
+%rename("") operator+=; // For Ruby and Octave that ignore operator+=
+
+%inline %{
+template<typename T, int dim> struct Foot {
+  template <template <typename, int> class X, typename U>
+    void operator+=(X<U, dim> & ref) {}
+};
+
+void TestInstantiationsPart3() {
+  Foot<int, 99> MyFootInt99;
+  MyFootInt99.operator+=<Foot, int>(MyFootInt99);
+  MyFootInt99 += MyFootInt99;
+}
+%}
+
+%template(MyFootInt99) Foot<int, 99>;
+%extend Foot<int, 99> {
+  %template(OperatorPlusEquals) operator+=<Foot, int>;
+}
diff --git a/Examples/test-suite/template_template_template_parameters.i b/Examples/test-suite/template_template_template_parameters.i
new file mode 100644
index 000000000..a2588d3be
--- /dev/null
+++ b/Examples/test-suite/template_template_template_parameters.i
@@ -0,0 +1,45 @@
+%module template_template_template_parameters
+
+%inline %{
+// Github issue #624
+class CustomAttrs {
+public:
+  enum dattr1d {pos, vel, someCustomCaseVar, d1dLast};
+};
+
+template <class TT> 
+class A {
+public:
+  TT attributes;
+};
+
+template <template<class> class A, class T> 
+class B : public A<T> {
+public:
+  virtual void BMethod(T t_parm, A<T> at_parm) {}
+};
+
+template <template<template<class> class, class> class Op, template<class> class X, class Y>
+class C : public Op<X,Y> {
+public:
+  virtual void CMethod(Y y_parm, Op<X, Y> opxy_parm) {}
+};
+
+template <template<template<class K1> class K2, class K3> class L, template<class K4> class M, class N>
+class D : public L<M,N> {
+public:
+  virtual void DMethod(N n_parm, L<M, N> lmn_parm) {}
+};
+%}
+
+%{
+template class A<CustomAttrs>;
+template class B<A, CustomAttrs>;
+template class C<B, A, CustomAttrs>;
+template class D<B, A, CustomAttrs>;
+%}
+
+%template(AC) A<CustomAttrs>;
+%template(BAC) B<A, CustomAttrs>;
+%template(CBAC) C<B, A, CustomAttrs>;
+%template(DBAC) D<B, A, CustomAttrs>;
diff --git a/Source/CParse/parser.y b/Source/CParse/parser.y
index 526d65ff6..c0f1394d8 100644
--- a/Source/CParse/parser.y
+++ b/Source/CParse/parser.y
@@ -1681,7 +1681,7 @@ static String *add_qualifier_to_declarator(SwigType *type, SwigType *qualifier)
 %type <dtype>    initializer cpp_const exception_specification cv_ref_qualifier qualifiers_exception_specification;
 %type <id>       storage_class extern_string;
 %type <pl>       parms  ptail rawparms varargs_parms ;
-%type <pl>       templateparameters templateparameterstail;
+%type <pl>       templateparameterstail;
 %type <p>        parm_no_dox parm valparm rawvalparms valparms valptail ;
 %type <p>        typemap_parm tm_list tm_tail ;
 %type <p>        templateparameter ;
@@ -4446,43 +4446,7 @@ cpp_template_possible:  c_decl {
                 }
                 ;
 
-template_parms  : templateparameters {
-		   /* Rip out the parameter names */
-		  Parm *p = $1;
-		  $$ = $1;
-
-		  while (p) {
-		    String *name = Getattr(p,"name");
-		    if (!name) {
-		      /* Hmmm. Maybe it's a 'class T' parameter */
-		      char *type = Char(Getattr(p,"type"));
-		      /* Template template parameter */
-		      if (strncmp(type,"template<class> ",16) == 0) {
-			type += 16;
-		      }
-		      if ((strncmp(type,"class ",6) == 0) || (strncmp(type,"typename ", 9) == 0)) {
-			char *t = strchr(type,' ');
-			Setattr(p,"name", t+1);
-		      } else 
-                      /* Variadic template args */
-		      if ((strncmp(type,"class... ",9) == 0) || (strncmp(type,"typename... ", 12) == 0)) {
-			char *t = strchr(type,' ');
-			Setattr(p,"name", t+1);
-			Setattr(p,"variadic", "1");
-		      } else {
-			/*
-			 Swig_error(cparse_file, cparse_line, "Missing template parameter name\n");
-			 $$.rparms = 0;
-			 $$.parms = 0;
-			 break; */
-		      }
-		    }
-		    p = nextSibling(p);
-		  }
-                 }
-                 ;
-
-templateparameters : templateparameter templateparameterstail {
+template_parms : templateparameter templateparameterstail {
                       set_nextSibling($1,$2);
                       $$ = $1;
                    }
@@ -4491,10 +4455,52 @@ templateparameters : templateparameter templateparameterstail {
 
 templateparameter : templcpptype def_args {
 		    $$ = NewParmWithoutFileLineInfo(NewString($1), 0);
+		    previousNode = currentNode;
+		    currentNode = $$;
+		    Setfile($$, cparse_file);
+		    Setline($$, cparse_line);
 		    Setattr($$, "value", $2.rawval ? $2.rawval : $2.val);
-                  }
-                  | parm {
-                    $$ = $1;
+		  }
+		  | TEMPLATE LESSTHAN template_parms GREATERTHAN cpptype idcolon def_args {
+		    $$ = NewParmWithoutFileLineInfo(NewStringf("template< %s > %s %s", ParmList_str_defaultargs($3), $5, $6), $6);
+		    previousNode = currentNode;
+		    currentNode = $$;
+		    Setfile($$, cparse_file);
+		    Setline($$, cparse_line);
+		    if ($7.val) {
+		      Setattr($$, "value", $7.val);
+		    }
+		  }
+		  | TEMPLATE LESSTHAN template_parms GREATERTHAN cpptype def_args {
+		    $$ = NewParmWithoutFileLineInfo(NewStringf("template< %s > %s", ParmList_str_defaultargs($3), $5), 0);
+		    previousNode = currentNode;
+		    currentNode = $$;
+		    Setfile($$, cparse_file);
+		    Setline($$, cparse_line);
+		    if ($6.val) {
+		      Setattr($$, "value", $6.val);
+		    }
+		  }
+		  | parm {
+		    Parm *p = $1;
+		    $$ = $1;
+
+		    /* TODO: also slice off the name from the "type" */
+		    /* Rip out the parameter names */
+		    String *name = Getattr(p, "name");
+		    if (!name) {
+		      String *type = Getattr(p, "type");
+		      if ((Strncmp(type, "class ", 6) == 0) || (Strncmp(type, "typename ", 9) == 0)) {
+			/* A 'class T' parameter */
+			const char *t = Strchr(type, ' ');
+			Setattr(p, "name", t + 1);
+		      } else if ((Strncmp(type, "class... ", 9) == 0) || (Strncmp(type, "typename... ", 12) == 0)) {
+			/* Variadic template args */
+			const char *t = Strchr(type, ' ');
+			Setattr(p, "name", t + 1);
+			Setattr(p, "variadic", "1");
+		      }
+		    }
                   }
                   ;
 
@@ -5195,17 +5201,6 @@ parm_no_dox	: rawtype parameter_declarator {
 		     Setattr($$,"value",$2.defarg);
 		   }
 		}
-
-                | TEMPLATE LESSTHAN cpptype GREATERTHAN cpptype idcolon def_args {
-                  $$ = NewParmWithoutFileLineInfo(NewStringf("template<class> %s %s", $5,$6), 0);
-		  previousNode = currentNode;
-		  currentNode = $$;
-		  Setfile($$,cparse_file);
-		  Setline($$,cparse_line);
-                  if ($7.val) {
-                    Setattr($$,"value",$7.val);
-                  }
-                }
                 | ELLIPSIS {
 		  SwigType *t = NewString("v(...)");
 		  $$ = NewParmWithoutFileLineInfo(t, 0);