diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/Call/ArgumentAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/Expression/Call/ArgumentAnalyzer.php
index 3ab280d42..aceea26be 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/Call/ArgumentAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/Call/ArgumentAnalyzer.php
@@ -257,15 +257,26 @@ class ArgumentAnalyzer
         );
 
         if ($class_generic_params) {
-            $empty_generic_params = [];
+            // here we're replacing the param types and arg types with the bound
+            // class template params.
+            //
+            // For example, if we're operating on a class Foo with params TKey and TValue,
+            // and we're calling a method "add(TKey $key, TValue $value)" on an instance
+            // of that class where we know that TKey is int and TValue is string, then we
+            // want to replace the substitute the expected values so it's as if we were actually
+            // calling "add(int $key, string $value)"
+            $readonly_template_result = new TemplateResult($class_generic_params, []);
 
-            $empty_template_result = new TemplateResult($class_generic_params, $empty_generic_params);
+            // This flag ensures that the template results will never be written to
+            // It also supercedes the `$add_upper_bounds` flag so that closure params
+            // don’t get overwritten
+            $readonly_template_result->readonly = true;
 
             $arg_value_type = $statements_analyzer->node_data->getType($arg->value);
 
             $param_type = TemplateStandinTypeReplacer::replace(
                 $param_type,
-                $empty_template_result,
+                $readonly_template_result,
                 $codebase,
                 $statements_analyzer,
                 $arg_value_type,
@@ -275,7 +286,7 @@ class ArgumentAnalyzer
 
             $arg_type = TemplateStandinTypeReplacer::replace(
                 $arg_type,
-                $empty_template_result,
+                $readonly_template_result,
                 $codebase,
                 $statements_analyzer,
                 $arg_value_type,
diff --git a/src/Psalm/Internal/Type/TemplateResult.php b/src/Psalm/Internal/Type/TemplateResult.php
index d327c7837..8806fc6ad 100644
--- a/src/Psalm/Internal/Type/TemplateResult.php
+++ b/src/Psalm/Internal/Type/TemplateResult.php
@@ -22,6 +22,13 @@ class TemplateResult
      */
     public $lower_bounds = [];
 
+    /**
+     * If set to true then we shouldn't update the template bounds
+     *
+     * @var bool
+     */
+    public $readonly = false;
+
     /**
      * @var list<Union>
      */
diff --git a/src/Psalm/Internal/Type/TemplateStandinTypeReplacer.php b/src/Psalm/Internal/Type/TemplateStandinTypeReplacer.php
index 385b0df62..518067b31 100644
--- a/src/Psalm/Internal/Type/TemplateStandinTypeReplacer.php
+++ b/src/Psalm/Internal/Type/TemplateStandinTypeReplacer.php
@@ -619,6 +619,7 @@ class TemplateStandinTypeReplacer
             );
 
             if ($input_type
+                && !$template_result->readonly
                 && (
                     $atomic_type->as->isMixed()
                     || !$codebase
@@ -686,20 +687,23 @@ class TemplateStandinTypeReplacer
                 );
             }
 
-            foreach ($atomic_types as $atomic_type) {
+            foreach ($atomic_types as &$atomic_type) {
                 if ($atomic_type instanceof Atomic\TNamedObject
                     || $atomic_type instanceof Atomic\TTemplateParam
                     || $atomic_type instanceof Atomic\TIterable
                     || $atomic_type instanceof Atomic\TObjectWithProperties
                 ) {
                     $atomic_type->extra_types = $extra_types;
+                } elseif ($atomic_type instanceof Atomic\TObject && $extra_types) {
+                    $atomic_type = \reset($extra_types);
+                    $atomic_type->extra_types = \array_slice($extra_types, 1);
                 }
             }
 
             return $atomic_types;
         }
 
-        if ($add_upper_bound && $input_type) {
+        if ($add_upper_bound && $input_type && !$template_result->readonly) {
             $matching_input_keys = [];
 
             if ($codebase
@@ -782,7 +786,7 @@ class TemplateStandinTypeReplacer
 
         $atomic_types[] = $class_string;
 
-        if ($input_type) {
+        if ($input_type && !$template_result->readonly) {
             $valid_input_atomic_types = [];
 
             foreach ($input_type->getAtomicTypes() as $input_atomic_type) {
diff --git a/tests/Template/ClassTemplateTest.php b/tests/Template/ClassTemplateTest.php
index 74e7d51a1..f8294670e 100644
--- a/tests/Template/ClassTemplateTest.php
+++ b/tests/Template/ClassTemplateTest.php
@@ -2394,21 +2394,18 @@ class ClassTemplateTest extends TestCase
             'intersectOnTOfObject' => [
                 '<?php
                     /**
-                     * @psalm-template InterceptedObjectType of object
+                     * @psalm-template TO of object
                      */
-                    interface AccessInterceptorInterface
-                    {
+                    interface A {
                         /**
-                         * @psalm-param Closure(
-                         *   InterceptedObjectType&AccessInterceptorInterface
-                         * ) : mixed $prefixInterceptor
+                         * @psalm-param Closure(TO&A):mixed $c
                          */
-                        public function setMethodPrefixInterceptor(Closure $prefixInterceptor = null) : void;
+                        public function setClosure(Closure $c): void;
                     }
 
-                    function foo(AccessInterceptorInterface $i) : void {
-                        $i->setMethodPrefixInterceptor(
-                            function(AccessInterceptorInterface $i) : string {
+                    function foo(A $i) : void {
+                        $i->setClosure(
+                            function(A $i) : string {
                                 return "hello";
                             }
                         );
@@ -3801,6 +3798,31 @@ class ClassTemplateTest extends TestCase
                 false,
                 '8.0'
             ],
+            'bindClosureParamAccurately' => [
+                '<?php
+                    /**
+                     * @template TKey
+                     * @template TValue
+                     */
+                    interface Collection {
+                        /**
+                         * @template T
+                         * @param Closure(TValue):T $func
+                         * @return Collection<TKey,T>
+                         */
+                        public function map(Closure $func);
+
+                    }
+
+                    /**
+                     * @param Collection<int, string> $c
+                     */
+                    function f(Collection $c): void {
+                        $fn = function(int $_p): bool { return true; };
+                        $c->map($fn);
+                    }',
+                'error_message' => 'InvalidScalarArgument',
+            ],
         ];
     }
 }