diff --git a/src/cache/multilevel.rs b/src/cache/multilevel.rs
index 7c75bda3f..a5c7d5211 100644
--- a/src/cache/multilevel.rs
+++ b/src/cache/multilevel.rs
@@ -877,14 +877,22 @@ impl Storage for MultiLevelStorage {
     }
 
     async fn check(&self) -> Result<CacheMode> {
-        let mut result = CacheMode::ReadWrite;
+        // The composite is writable when any level is writable: put()
+        // already skips read-only levels on writes, so a read-only level
+        // must not demote the whole chain (e.g. a writable local disk in
+        // front of a read-only shared remote). Only a chain in which
+        // every level is read-only is itself read-only.
+        let mut result = CacheMode::ReadOnly;
+        if self.levels.is_empty() {
+            return Ok(CacheMode::ReadWrite);
+        }
         for (idx, level) in self.levels.iter().enumerate() {
             match level.check().await {
                 Ok(CacheMode::ReadOnly) => {
-                    result = CacheMode::ReadOnly;
                     debug!("Cache level {} is read-only", idx);
                 }
                 Ok(CacheMode::ReadWrite) => {
+                    result = CacheMode::ReadWrite;
                     trace!("Cache level {} is read-write", idx);
                 }
                 Err(e) => {
@@ -893,6 +901,7 @@ impl Storage for MultiLevelStorage {
                 }
             }
         }
+        debug!("Multi-level cache mode: {:?}", result);
         Ok(result)
     }
 
diff --git a/src/cache/multilevel_test.rs b/src/cache/multilevel_test.rs
index b75f6d3fa..0845d6fc3 100644
--- a/src/cache/multilevel_test.rs
+++ b/src/cache/multilevel_test.rs
@@ -970,6 +970,63 @@ fn test_readonly_level_in_check() {
     });
 }
 
+#[test]
+fn test_mixed_readonly_chain_is_readwrite_in_check() {
+    // A chain that contains a writable level must report ReadWrite even
+    // when other levels are read-only: put() skips read-only levels, so a
+    // read-only remote behind a writable local disk (the documented
+    // "read-only fallback" topology) must not demote the whole cache to
+    // read-only. Regression test for #2773.
+    let runtime = RuntimeBuilder::new_current_thread()
+        .enable_all()
+        .build()
+        .unwrap();
+
+    // Writable L0, read-only L1
+    let rw_l0 = Arc::new(InMemoryStorage::new());
+    let ro_l1 = Arc::new(ReadOnlyStorage(Arc::new(InMemoryStorage::new())));
+    let storage =
+        MultiLevelStorage::new(vec![rw_l0 as Arc<dyn Storage>, ro_l1 as Arc<dyn Storage>]);
+    runtime.block_on(async {
+        match storage.check().await.unwrap() {
+            CacheMode::ReadWrite => {} // Expected
+            _ => panic!("Writable L0 + read-only L1 should be ReadWrite"),
+        }
+    });
+
+    // Read-only L0, writable L1: still writable (put() skips L0)
+    let ro_l0 = Arc::new(ReadOnlyStorage(Arc::new(InMemoryStorage::new())));
+    let rw_l1 = Arc::new(InMemoryStorage::new());
+    let storage =
+        MultiLevelStorage::new(vec![ro_l0 as Arc<dyn Storage>, rw_l1 as Arc<dyn Storage>]);
+    runtime.block_on(async {
+        match storage.check().await.unwrap() {
+            CacheMode::ReadWrite => {} // Expected
+            _ => panic!("Read-only L0 + writable L1 should be ReadWrite"),
+        }
+    });
+}
+
+#[test]
+fn test_all_readonly_chain_is_readonly_in_check() {
+    // Only a chain in which EVERY level is read-only is itself read-only.
+    let runtime = RuntimeBuilder::new_current_thread()
+        .enable_all()
+        .build()
+        .unwrap();
+
+    let ro_l0 = Arc::new(ReadOnlyStorage(Arc::new(InMemoryStorage::new())));
+    let ro_l1 = Arc::new(ReadOnlyStorage(Arc::new(InMemoryStorage::new())));
+    let storage =
+        MultiLevelStorage::new(vec![ro_l0 as Arc<dyn Storage>, ro_l1 as Arc<dyn Storage>]);
+    runtime.block_on(async {
+        match storage.check().await.unwrap() {
+            CacheMode::ReadOnly => {} // Expected
+            _ => panic!("All read-only levels should be ReadOnly"),
+        }
+    });
+}
+
 #[test]
 fn test_sequential_read_order() {
     // Test that reads happen sequentially (L0, L1, L2, ...), not in parallel