diff --git a/llvm/include/llvm/Analysis/CGSCCPassManager.h b/llvm/include/llvm/Analysis/CGSCCPassManager.h
--- a/llvm/include/llvm/Analysis/CGSCCPassManager.h
+++ b/llvm/include/llvm/Analysis/CGSCCPassManager.h
@@ -487,8 +487,16 @@
   void printPipeline(raw_ostream &OS,
                      function_ref<StringRef(StringRef)> MapClassName2PassName) {
     OS << "function";
-    if (EagerlyInvalidate)
-      OS << "<eager-inv>";
+    if (EagerlyInvalidate || NoRerun) {
+      OS << "<";
+      if (EagerlyInvalidate)
+        OS << "eager-inv";
+      if (EagerlyInvalidate && NoRerun)
+        OS << ";";
+      if (NoRerun)
+        OS << "no-rerun";
+      OS << ">";
+    }
     OS << '(';
     Pass->printPipeline(OS, MapClassName2PassName);
     OS << ')';
diff --git a/llvm/lib/Passes/PassBuilder.cpp b/llvm/lib/Passes/PassBuilder.cpp
--- a/llvm/lib/Passes/PassBuilder.cpp
+++ b/llvm/lib/Passes/PassBuilder.cpp
@@ -486,6 +486,28 @@
   return Count;
 }
 
+static std::optional<std::pair<bool, bool>>
+parseFunctionPipelineName(StringRef Name) {
+  std::pair<bool, bool> Params;
+  if (!Name.consume_front("function"))
+    return std::nullopt;
+  if (Name.empty())
+    return Params;
+  if (!Name.consume_front("<") || !Name.consume_back(">"))
+    return std::nullopt;
+  while (!Name.empty()) {
+    auto [Front, Back] = Name.split(';');
+    Name = Back;
+    if (Front == "eager-inv")
+      Params.first = true;
+    else if (Front == "no-rerun")
+      Params.second = true;
+    else
+      return std::nullopt;
+  }
+  return Params;
+}
+
 static std::optional<int> parseDevirtPassName(StringRef Name) {
   if (!Name.consume_front("devirt<") || !Name.consume_back(">"))
     return std::nullopt;
@@ -1009,12 +1031,14 @@
   if (startsWithDefaultPipelineAliasPrefix(Name))
     return DefaultAliasRegex.match(Name);
 
+  StringRef NameNoBracket = Name.take_until([](char C) { return C == '<'; });
+
   // Explicitly handle pass manager names.
   if (Name == "module")
     return true;
   if (Name == "cgscc")
     return true;
-  if (Name == "function" || Name == "function<eager-inv>")
+  if (NameNoBracket == "function")
     return true;
   if (Name == "coro-cond")
     return true;
@@ -1040,9 +1064,10 @@
 template <typename CallbacksT>
 static bool isCGSCCPassName(StringRef Name, CallbacksT &Callbacks) {
   // Explicitly handle pass manager names.
+  StringRef NameNoBracket = Name.take_until([](char C) { return C == '<'; });
   if (Name == "cgscc")
     return true;
-  if (Name == "function" || Name == "function<eager-inv>")
+  if (NameNoBracket == "function")
     return true;
 
   // Explicitly handle custom-parsed pass names.
@@ -1068,7 +1093,8 @@
 template <typename CallbacksT>
 static bool isFunctionPassName(StringRef Name, CallbacksT &Callbacks) {
   // Explicitly handle pass manager names.
-  if (Name == "function" || Name == "function<eager-inv>")
+  StringRef NameNoBracket = Name.take_until([](char C) { return C == '<'; });
+  if (NameNoBracket == "function")
     return true;
   if (Name == "loop" || Name == "loop-mssa")
     return true;
@@ -1226,12 +1252,16 @@
       MPM.addPass(createModuleToPostOrderCGSCCPassAdaptor(std::move(CGPM)));
       return Error::success();
     }
-    if (Name == "function" || Name == "function<eager-inv>") {
+    if (auto Params = parseFunctionPipelineName(Name)) {
+      if (Params->second)
+        return make_error<StringError>(
+            "cannot have a no-rerun module to function adaptor",
+            inconvertibleErrorCode());
       FunctionPassManager FPM;
       if (auto Err = parseFunctionPassPipeline(FPM, InnerPipeline))
         return Err;
-      MPM.addPass(createModuleToFunctionPassAdaptor(std::move(FPM),
-                                                    Name != "function"));
+      MPM.addPass(
+          createModuleToFunctionPassAdaptor(std::move(FPM), Params->first));
       return Error::success();
     }
     if (auto Count = parseRepeatPassName(Name)) {
@@ -1394,13 +1424,13 @@
       CGPM.addPass(std::move(NestedCGPM));
       return Error::success();
     }
-    if (Name == "function" || Name == "function<eager-inv>") {
+    if (auto Params = parseFunctionPipelineName(Name)) {
       FunctionPassManager FPM;
       if (auto Err = parseFunctionPassPipeline(FPM, InnerPipeline))
         return Err;
       // Add the nested pass manager with the appropriate adaptor.
-      CGPM.addPass(
-          createCGSCCToFunctionPassAdaptor(std::move(FPM), Name != "function"));
+      CGPM.addPass(createCGSCCToFunctionPassAdaptor(
+          std::move(FPM), Params->first, Params->second));
       return Error::success();
     }
     if (auto Count = parseRepeatPassName(Name)) {
diff --git a/llvm/test/Other/new-pm-print-pipeline.ll b/llvm/test/Other/new-pm-print-pipeline.ll
--- a/llvm/test/Other/new-pm-print-pipeline.ll
+++ b/llvm/test/Other/new-pm-print-pipeline.ll
@@ -101,3 +101,13 @@
 ;; Test function-attrs
 ; RUN: opt -disable-output -disable-verify -print-pipeline-passes -passes='cgscc(function-attrs<skip-non-recursive>)' < %s | FileCheck %s --match-full-lines --check-prefixes=CHECK-29
 ; CHECK-29: cgscc(function-attrs<skip-non-recursive>)
+
+;; Test cgscc -> function adaptor
+; RUN: opt -disable-output -disable-verify -print-pipeline-passes -passes='cgscc(function<eager-inv;no-rerun>(no-op-function))' < %s | FileCheck %s --match-full-lines --check-prefixes=CHECK-30
+; CHECK-30: cgscc(function<eager-inv;no-rerun>(no-op-function))
+
+; RUN: opt -disable-output -disable-verify -print-pipeline-passes -passes='cgscc(function<no-rerun;eager-inv>(no-op-function))' < %s | FileCheck %s --match-full-lines --check-prefixes=CHECK-31
+; CHECK-31: cgscc(function<eager-inv;no-rerun>(no-op-function))
+
+; RUN: opt -disable-output -disable-verify -print-pipeline-passes -passes='cgscc(function<no-rerun>(no-op-function))' < %s | FileCheck %s --match-full-lines --check-prefixes=CHECK-32
+; CHECK-32: cgscc(function<no-rerun>(no-op-function))
diff --git a/llvm/test/Other/pass-pipeline-parsing.ll b/llvm/test/Other/pass-pipeline-parsing.ll
--- a/llvm/test/Other/pass-pipeline-parsing.ll
+++ b/llvm/test/Other/pass-pipeline-parsing.ll
@@ -57,6 +57,10 @@
 ; CHECK-DEFAULT-AA-DAG: Running analysis: BasicAA
 ; CHECK-DEFAULT-AA-DAG: Running analysis: TypeBasedAA
 
+; RUN: not opt -passes='function<no-rerun>(no-op-function)' %s 2>&1 \
+; RUN:     | FileCheck %s --check-prefix=CHECK-RERUN-BAD
+; CHECK-RERUN-BAD: cannot have a no-rerun module to function adaptor
+
 ; RUN: not opt -disable-output -debug-pass-manager \
 ; RUN:     -passes='no-op-module)' %s 2>&1 \
 ; RUN:     | FileCheck %s --check-prefix=CHECK-UNBALANCED1