diff --git a/src/dvc_objects/db.py b/src/dvc_objects/db.py
index ae1d667..6ed8cde 100644
--- a/src/dvc_objects/db.py
+++ b/src/dvc_objects/db.py
@@ -433,6 +433,7 @@ def oids_exist(self, oids, jobs=None, progress=noop):
             traverse_weight = traverse_pages * self.fs.TRAVERSE_WEIGHT_MULTIPLIER
         else:
             traverse_weight = traverse_pages
+        traverse_weight *= self.fs.EXTRA_TRAVERSE_WEIGHT_MULTIPLIER
         if len(oids) < traverse_weight and not always_traverse:
             logger.debug(
                 "Large remote (%r oids < %r traverse weight), "
diff --git a/src/dvc_objects/fs/base.py b/src/dvc_objects/fs/base.py
index 6ad1b07..10fe29b 100644
--- a/src/dvc_objects/fs/base.py
+++ b/src/dvc_objects/fs/base.py
@@ -69,6 +69,9 @@ class FileSystem:
     HASH_JOBS = max(1, min(4, cpu_count() // 2))
     LIST_OBJECT_PAGE_SIZE = 1000
     TRAVERSE_WEIGHT_MULTIPLIER = 5
+    EXTRA_TRAVERSE_WEIGHT_MULTIPLIER = int(
+        os.getenv("EXTRA_TRAVERSE_WEIGHT_MULTIPLIER", "1")
+    )
     TRAVERSE_PREFIX_LEN = 2
     TRAVERSE_THRESHOLD_SIZE = 500000
     CAN_TRAVERSE = True