diff --git a/src/humanize/filesize.py b/src/humanize/filesize.py
index fb675fd..cf09f1e 100644
--- a/src/humanize/filesize.py
+++ b/src/humanize/filesize.py
@@ -42,6 +42,8 @@ def naturalsize(
     binary: bool = False,
     gnu: bool = False,
     format: str = "%.1f",
+    *,
+    rollover: bool = True,
 ) -> str:
     """Format a number of bytes like a human-readable filesize (e.g. 10 kB).
 
@@ -77,6 +79,7 @@ def naturalsize(
         gnu (bool): If `True`, the binary argument is ignored and GNU-style
             (`ls -sh` style) prefixes are used (K, M) with the 2**10 definition.
         format (str): Custom formatter.
+        rollover (bool): Promote a rounded mantissa to the next suffix when available.
 
     Returns:
         str: Human readable representation of a filesize.
@@ -103,7 +106,11 @@ def naturalsize(
     # mantissa afterward; rounding can push it up to `base` (e.g. 999999 is
     # 999.999 kB, which formats to "1000.0 kB"). When that happens and a larger
     # suffix is available, step up one suffix so the result reads "1.0 MB".
-    if exp < len(suffix) and abs(float(format % (abs_bytes / (base**exp)))) >= base:
+    if (
+        rollover
+        and exp < len(suffix)
+        and abs(float(format % (abs_bytes / (base**exp)))) >= base
+    ):
         exp += 1
     space = "" if gnu else " "
     ret: str = format % (bytes_ / (base**exp)) + space + _(suffix[exp - 1])