diff --git a/clippy_lints/src/methods/map_identity.rs b/clippy_lints/src/methods/map_identity.rs
index 98def66ca149..6497cdcaf11c 100644
--- a/clippy_lints/src/methods/map_identity.rs
+++ b/clippy_lints/src/methods/map_identity.rs
@@ -1,9 +1,8 @@
-use clippy_utils::diagnostics::span_lint_and_sugg;
+use clippy_utils::diagnostics::span_lint_and_then;
 use clippy_utils::ty::is_type_diagnostic_item;
-use clippy_utils::{is_expr_untyped_identity_function, is_trait_method, path_to_local};
-use rustc_ast::BindingMode;
+use clippy_utils::{is_expr_untyped_identity_function, is_mutable, is_trait_method, path_to_local};
 use rustc_errors::Applicability;
-use rustc_hir::{self as hir, Node, PatKind};
+use rustc_hir::{self as hir, ExprKind, Node, PatKind};
 use rustc_lint::LateContext;
 use rustc_span::{Span, Symbol, sym};
 
@@ -23,26 +22,57 @@ pub(super) fn check(
         || is_type_diagnostic_item(cx, caller_ty, sym::Result)
         || is_type_diagnostic_item(cx, caller_ty, sym::Option))
         && is_expr_untyped_identity_function(cx, map_arg)
-        && let Some(sugg_span) = expr.span.trim_start(caller.span)
+        && let Some(call_span) = expr.span.trim_start(caller.span)
     {
-        // If the result of `.map(identity)` is used as a mutable reference,
-        // the caller must not be an immutable binding.
-        if cx.typeck_results().expr_ty_adjusted(expr).is_mutable_ptr()
-            && let Some(hir_id) = path_to_local(caller)
-            && let Node::Pat(pat) = cx.tcx.hir_node(hir_id)
-            && !matches!(pat.kind, PatKind::Binding(BindingMode::MUT, ..))
-        {
-            return;
+        let mut sugg = vec![(call_span, String::new())];
+        let mut apply = true;
+        if !is_mutable(cx, caller) {
+            if let Some(hir_id) = path_to_local(caller)
+                && let Node::Pat(pat) = cx.tcx.hir_node(hir_id)
+                && let PatKind::Binding(_, _, ident, _) = pat.kind
+            {
+                sugg.push((ident.span.shrink_to_lo(), String::from("mut ")));
+            } else {
+                // If we can't make the binding mutable, make the suggestion `Unspecified` to prevent it from being
+                // automatically applied, and add a complementary help message.
+                apply = false;
+            }
         }
 
-        span_lint_and_sugg(
+        let method_requiring_mut = if let Node::Expr(expr) = cx.tcx.parent_hir_node(expr.hir_id)
+            && let ExprKind::MethodCall(method, ..) = expr.kind
+        {
+            Some(method.ident)
+        } else {
+            None
+        };
+
+        span_lint_and_then(
             cx,
             MAP_IDENTITY,
-            sugg_span,
+            call_span,
             "unnecessary map of the identity function",
-            format!("remove the call to `{name}`"),
-            String::new(),
-            Applicability::MachineApplicable,
+            |diag| {
+                diag.multipart_suggestion(
+                    format!("remove the call to `{name}`"),
+                    sugg,
+                    if apply {
+                        Applicability::MachineApplicable
+                    } else {
+                        Applicability::Unspecified
+                    },
+                );
+                if !apply {
+                    if let Some(method_requiring_mut) = method_requiring_mut {
+                        diag.span_note(
+                            caller.span,
+                            format!("this must be made mutable to use `{method_requiring_mut}`"),
+                        );
+                    } else {
+                        diag.span_note(caller.span, "this must be made mutable".to_string());
+                    }
+                }
+            },
         );
     }
 }
diff --git a/tests/ui/map_identity.fixed b/tests/ui/map_identity.fixed
index b82d3e6d9567..00e626eeb24a 100644
--- a/tests/ui/map_identity.fixed
+++ b/tests/ui/map_identity.fixed
@@ -72,9 +72,12 @@ fn issue11764() {
 }
 
 fn issue13904() {
-    // don't lint: `it.next()` would not be legal as `it` is immutable
-    let it = [1, 2, 3].into_iter();
-    let _ = it.map(|x| x).next();
+    // lint, but there's a catch:
+    // when we remove the `.map()`, `it.next()` would require `it` to be mutable
+    // therefore, include that in the suggestion as well
+    let mut it = [1, 2, 3].into_iter();
+    let _ = it.next();
+    //~^ map_identity
 
     // lint
     #[allow(unused_mut)]
diff --git a/tests/ui/map_identity.rs b/tests/ui/map_identity.rs
index c295bf872701..fbffccfbb9ee 100644
--- a/tests/ui/map_identity.rs
+++ b/tests/ui/map_identity.rs
@@ -78,9 +78,12 @@ fn issue11764() {
 }
 
 fn issue13904() {
-    // don't lint: `it.next()` would not be legal as `it` is immutable
+    // lint, but there's a catch:
+    // when we remove the `.map()`, `it.next()` would require `it` to be mutable
+    // therefore, include that in the suggestion as well
     let it = [1, 2, 3].into_iter();
     let _ = it.map(|x| x).next();
+    //~^ map_identity
 
     // lint
     #[allow(unused_mut)]
diff --git a/tests/ui/map_identity.stderr b/tests/ui/map_identity.stderr
index 9b624a0dc755..6bdbfde09ae8 100644
--- a/tests/ui/map_identity.stderr
+++ b/tests/ui/map_identity.stderr
@@ -76,22 +76,34 @@ LL |     let _ = x.iter().copied().map(|(x, y)| (x, y));
    |                              ^^^^^^^^^^^^^^^^^^^^^ help: remove the call to `map`
 
 error: unnecessary map of the identity function
-  --> tests/ui/map_identity.rs:88:15
+  --> tests/ui/map_identity.rs:85:15
+   |
+LL |     let _ = it.map(|x| x).next();
+   |               ^^^^^^^^^^^
+   |
+help: remove the call to `map`
+   |
+LL ~     let mut it = [1, 2, 3].into_iter();
+LL ~     let _ = it.next();
+   |
+
+error: unnecessary map of the identity function
+  --> tests/ui/map_identity.rs:91:15
    |
 LL |     let _ = it.map(|x| x).next();
    |               ^^^^^^^^^^^ help: remove the call to `map`
 
 error: unnecessary map of the identity function
-  --> tests/ui/map_identity.rs:93:19
+  --> tests/ui/map_identity.rs:96:19
    |
 LL |     let _ = { it }.map(|x| x).next();
    |                   ^^^^^^^^^^^ help: remove the call to `map`
 
 error: unnecessary map of the identity function
-  --> tests/ui/map_identity.rs:105:30
+  --> tests/ui/map_identity.rs:108:30
    |
 LL |     let _ = x.iter().copied().map(|[x, y]| [x, y]);
    |                              ^^^^^^^^^^^^^^^^^^^^^ help: remove the call to `map`
 
-error: aborting due to 14 previous errors
+error: aborting due to 15 previous errors
 
diff --git a/tests/ui/map_identity_unfixable.rs b/tests/ui/map_identity_unfixable.rs
new file mode 100644
index 000000000000..5a5106e76d16
--- /dev/null
+++ b/tests/ui/map_identity_unfixable.rs
@@ -0,0 +1,9 @@
+//@no-rustfix
+#![warn(clippy::map_identity)]
+
+fn main() {
+    let mut index = [true, true, false, false, false, true].iter();
+    let subindex = (index.by_ref().take(3), 42);
+    let _ = subindex.0.map(|n| n).next();
+    //~^ map_identity
+}
diff --git a/tests/ui/map_identity_unfixable.stderr b/tests/ui/map_identity_unfixable.stderr
new file mode 100644
index 000000000000..4d6a46df41cc
--- /dev/null
+++ b/tests/ui/map_identity_unfixable.stderr
@@ -0,0 +1,16 @@
+error: unnecessary map of the identity function
+  --> tests/ui/map_identity_unfixable.rs:7:23
+   |
+LL |     let _ = subindex.0.map(|n| n).next();
+   |                       ^^^^^^^^^^^ help: remove the call to `map`
+   |
+note: this must be made mutable to use `next`
+  --> tests/ui/map_identity_unfixable.rs:7:13
+   |
+LL |     let _ = subindex.0.map(|n| n).next();
+   |             ^^^^^^^^^^
+   = note: `-D clippy::map-identity` implied by `-D warnings`
+   = help: to override `-D warnings` add `#[allow(clippy::map_identity)]`
+
+error: aborting due to 1 previous error
+