diff --git a/src/schema/rules/checks/general.yaml b/src/schema/rules/checks/general.yaml
index 3c03bac91d..653a3a8cff 100644
--- a/src/schema/rules/checks/general.yaml
+++ b/src/schema/rules/checks/general.yaml
@@ -20,6 +20,18 @@ ReadmeFileSmall:
       Please consider expanding it with additional information about the dataset.
     level: warning
   selectors:
-    - match(path, '^/README')
+    - match(path, '^/README.*')
   checks:
     - size > 150
+
+DuplicateReadmes:
+  issues:
+    code: MULTIPLE_README_FILES
+    message: |
+      There are multiple '/README' files (with different extensions) in this BIDS
+      dataset. Only one '/README' file should exist.
+    level: error
+  selectors:
+    - match(path, '^/README.*')
+  checks:
+    - exists(["README", "README.md", "README.rst", "README.txt"], "dataset") == 1