Index: clang/lib/Format/TokenAnnotator.cpp
===================================================================
--- clang/lib/Format/TokenAnnotator.cpp
+++ clang/lib/Format/TokenAnnotator.cpp
@@ -2281,6 +2281,10 @@
         Next = Next->Next;
         continue;
       }
+      if (Next->is(TT_TemplateOpener) && Next->MatchingParen) {
+        Next = Next->MatchingParen;
+        continue;
+      }
 
       break;
     }
@@ -2810,6 +2814,8 @@
                                     tok::l_square));
   if (Right.is(tok::star) && Left.is(tok::l_paren))
     return false;
+  if (Right.is(tok::star) && Left.is(tok::star))
+    return false;
   if (Right.isOneOf(tok::star, tok::amp, tok::ampamp)) {
     const FormatToken *Previous = &Left;
     while (Previous && !Previous->is(tok::kw_operator)) {
Index: clang/unittests/Format/FormatTest.cpp
===================================================================
--- clang/unittests/Format/FormatTest.cpp
+++ clang/unittests/Format/FormatTest.cpp
@@ -6279,7 +6279,17 @@
                "void\n"
                "A::operator[]() {}\n"
                "void\n"
-               "A::operator!() {}\n",
+               "A::operator!() {}\n"
+               "void\n"
+               "A::operator**() {}\n"
+               "void\n"
+               "A::operator<Foo> *() {}\n"
+               "void\n"
+               "A::operator<Foo> **() {}\n"
+               "void\n"
+               "A::operator<Foo> &() {}\n"
+               "void\n"
+               "A::operator void **() {}\n",
                Style);
   verifyFormat("constexpr auto\n"
                "operator()() const -> reference {}\n"
@@ -6296,6 +6306,10 @@
                "constexpr auto\n"
                "operator void *() const -> reference {}\n"
                "constexpr auto\n"
+               "operator void **() const -> reference {}\n"
+               "constexpr auto\n"
+               "operator void *() const -> reference {}\n"
+               "constexpr auto\n"
                "operator void &() const -> reference {}\n"
                "constexpr auto\n"
                "operator void &&() const -> reference {}\n"
@@ -15628,9 +15642,20 @@
   Style.PointerAlignment = FormatStyle::PAS_Right;
   verifyFormat("Foo::operator*();", Style);
   verifyFormat("Foo::operator void *();", Style);
+  verifyFormat("Foo::operator void **();", Style);
   verifyFormat("Foo::operator()(void *);", Style);
   verifyFormat("Foo::operator*(void *);", Style);
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator**();", Style);
+  verifyFormat("Foo::operator&();", Style);
+  verifyFormat("Foo::operator<int> *();", Style);
+  verifyFormat("Foo::operator<Foo> *();", Style);
+  verifyFormat("Foo::operator<int> **();", Style);
+  verifyFormat("Foo::operator<Foo> **();", Style);
+  verifyFormat("Foo::operator<int> &();", Style);
+  verifyFormat("Foo::operator<Foo> &();", Style);
+  verifyFormat("Foo::operator<int> &&();", Style);
+  verifyFormat("Foo::operator<Foo> &&();", Style);
   verifyFormat("operator*(int (*)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&();", Style);
@@ -15641,21 +15666,39 @@
   verifyFormat("operator&(int (&)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&&();", Style);
+  verifyFormat("Foo::operator**();", Style);
   verifyFormat("Foo::operator void &&();", Style);
   verifyFormat("Foo::operator()(void &&);", Style);
   verifyFormat("Foo::operator&&(void &&);", Style);
   verifyFormat("Foo::operator&&();", Style);
   verifyFormat("operator&&(int(&&)(), class Foo);", Style);
+  verifyFormat("operator const nsTArrayRight<E> &()", Style);
+  verifyFormat("[[nodiscard]] operator const nsTArrayRight<E, Allocator> &()",
+               Style);
+  verifyFormat("operator void **()", Style);
+  verifyFormat("operator const FooRight<Object> &()", Style);
+  verifyFormat("operator const FooRight<Object> *()", Style);
+  verifyFormat("operator const FooRight<Object> **()", Style);
 
   Style.PointerAlignment = FormatStyle::PAS_Left;
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator**();", Style);
   verifyFormat("Foo::operator void*();", Style);
+  verifyFormat("Foo::operator void**();", Style);
   verifyFormat("Foo::operator/*comment*/ void*();", Style);
   verifyFormat("Foo::operator/*a*/ const /*b*/ void*();", Style);
   verifyFormat("Foo::operator/*a*/ volatile /*b*/ void*();", Style);
   verifyFormat("Foo::operator()(void*);", Style);
   verifyFormat("Foo::operator*(void*);", Style);
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator<int>*();", Style);
+  verifyFormat("Foo::operator<Foo>*();", Style);
+  verifyFormat("Foo::operator<int>**();", Style);
+  verifyFormat("Foo::operator<Foo>**();", Style);
+  verifyFormat("Foo::operator<int>&();", Style);
+  verifyFormat("Foo::operator<Foo>&();", Style);
+  verifyFormat("Foo::operator<int>&&();", Style);
+  verifyFormat("Foo::operator<Foo>&&();", Style);
   verifyFormat("operator*(int (*)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&();", Style);
@@ -15677,9 +15720,17 @@
   verifyFormat("Foo::operator&&(void&&);", Style);
   verifyFormat("Foo::operator&&();", Style);
   verifyFormat("operator&&(int(&&)(), class Foo);", Style);
+  verifyFormat("operator const nsTArrayLeft<E>&()", Style);
+  verifyFormat("[[nodiscard]] operator const nsTArrayLeft<E, Allocator>&()",
+               Style);
+  verifyFormat("operator void**()", Style);
+  verifyFormat("operator const FooLeft<Object>&()", Style);
+  verifyFormat("operator const FooLeft<Object>*()", Style);
+  verifyFormat("operator const FooLeft<Object>**()", Style);
 
   // PR45107
   verifyFormat("operator Vector<String>&();", Style);
+  verifyFormat("operator const Vector<String>&();", Style);
   verifyFormat("operator foo::Bar*();", Style);
   verifyFormat("operator const Foo<X>::Bar<Y>*();", Style);
   verifyFormat("operator/*a*/ const /*b*/ Foo /*c*/<X> /*d*/ ::Bar<Y>*();",