diff --git a/Tests/test_file_tiff_metadata.py b/Tests/test_file_tiff_metadata.py
index 2c41a264314..b42f0ec0ed5 100644
--- a/Tests/test_file_tiff_metadata.py
+++ b/Tests/test_file_tiff_metadata.py
@@ -484,6 +484,56 @@ def test_tag_offset() -> None:
         ifd.load(f)
 
 
+def test_tag_data_larger_than_file() -> None:
+    ifd = TiffImagePlugin.ImageFileDirectory_v2()
+
+    # Two BYTE tags that both claim the whole 30 byte IFD as their value.
+    tag_count = struct.pack("<H", 2)
+    tags = struct.pack("<HHLL", 0, 1, 30, 0) + struct.pack("<HHLL", 1, 1, 30, 0)
+    next_offset = struct.pack("<L", 0)
+
+    f = io.BytesIO(tag_count + tags + next_offset)
+    with pytest.warns(UserWarning, match="Tag data larger than file"):
+        ifd.load(f)
+    assert len(ifd[0]) == 30
+    assert 1 not in ifd
+
+
+def test_tag_data_larger_than_file_across_frames() -> None:
+    # Three 1x1 frames, each with a private BYTE tag that points to the same
+    # payload, which is more than half of the file.
+    payload_size = 400
+    ifd_size = 2 + 10 * 12 + 4
+    pixel_offset = 8 + payload_size
+    first_ifd = pixel_offset + 1
+
+    data = b"II*\x00" + struct.pack("<L", first_ifd)
+    data += b"Z" * payload_size + b"\x7f"
+    for i in range(3):
+        data += struct.pack("<H", 10)
+        for tag in (256, 257, 258, 259, 262, 277):
+            value = 8 if tag == 258 else 1
+            data += struct.pack("<HHLH2x", tag, 3, 1, value)
+        for tag, value in ((273, pixel_offset), (278, 1), (279, 1)):
+            data += struct.pack("<HHLL", tag, 4, 1, value)
+        data += struct.pack("<HHLL", 65000, 1, payload_size, 8)
+        data += struct.pack("<L", first_ifd + (i + 1) * ifd_size if i < 2 else 0)
+
+    with Image.open(io.BytesIO(data)) as im:
+        assert isinstance(im, TiffImagePlugin.TiffImageFile)
+        assert len(im.tag_v2[65000]) == payload_size
+
+        for frame in (1, 2):
+            with pytest.warns(UserWarning, match="Tag data larger than file"):
+                im.seek(frame)
+            assert 65000 not in im.tag_v2
+        assert im.n_frames == 3
+
+        # Reloading a frame gives the same tags as before
+        im.seek(0)
+        assert len(im.tag_v2[65000]) == payload_size
+
+
 def test_tag_group_data() -> None:
     base_ifd = TiffImagePlugin.ImageFileDirectory_v2()
     interop_ifd = TiffImagePlugin.ImageFileDirectory_v2(group=40965)
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index 35b490bd4e3..1383c81037b 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -622,6 +622,10 @@ def __init__(
         self.tagtype: dict[int, int] = {}
         """ Dictionary of tag types """
         self.reset()
+        # Maximum total out-of-line tag data that load() may read, as well
+        # as the size of the stream. Set by TiffImageFile so that
+        # all frames of a file share one budget.
+        self._tag_data_limit: int | None = None
         self.next = (
             self._unpack("Q", ifh[8:])[0]
             if self._bigtiff
@@ -895,6 +899,12 @@ def _ensure_read(self, fp: IO[bytes], size: int) -> bytes:
     def load(self, fp: IO[bytes]) -> None:
         self.reset()
         self._offset = fp.tell()
+        fp.seek(0, io.SEEK_END)
+        limit = fp.tell()
+        fp.seek(self._offset)
+        if self._tag_data_limit is not None:
+            limit = min(limit, self._tag_data_limit)
+        self._tag_data_size = 0
 
         try:
             tag_count = (
@@ -902,6 +912,7 @@ def load(self, fp: IO[bytes]) -> None:
                 if self._bigtiff
                 else self._unpack("H", self._ensure_read(fp, 2))
             )[0]
+            total_size = 0
             for i in range(tag_count):
                 tag, typ, count, data = (
                     self._unpack("HHQ8s", self._ensure_read(fp, 20))
@@ -928,6 +939,13 @@ def load(self, fp: IO[bytes]) -> None:
                     if offset >= 2**63:
                         warnings.warn("Tag offset too large")
                         continue
+                    # Well-formed IFD values should fit within the stream they
+                    # are read from, even before accounting for overlaps.
+                    total_size += size
+                    if total_size > limit:
+                        warnings.warn(f"Tag data larger than file. Skipping tag {tag}")
+                        continue
+                    self._tag_data_size += size
                     fp.seek(offset)
                     data = ImageFile._safe_read(fp, size)
                     fp.seek(here)
@@ -1207,6 +1225,13 @@ def _open(self) -> None:
         self._fp = self.fp
         self._frame_pos: list[int] = []
 
+        # Out-of-line tag data is budgeted across all frames, so that many
+        # frames cannot each read the same data. Each frame's limit is fixed
+        # when it is first loaded, so that reloading it gives the same tags.
+        self.fp.seek(0, io.SEEK_END)
+        self._tag_data_remaining = self.fp.tell()
+        self._tag_data_limits: list[int] = []
+
         logger.debug("*** TiffImageFile._open ***")
         logger.debug("- __first: %s", self.__first)
         logger.debug("- ifh: %s", repr(ifh))  # Use repr to avoid str(bytes)
@@ -1259,8 +1284,11 @@ def _seek(self, frame: int) -> None:
                 raise ValueError(msg)
             self.fp.seek(self.__next)
             self._frame_pos.append(self.__next)
+            self._tag_data_limits.append(self._tag_data_remaining)
             logger.debug("Loading tags, location: %s", self.fp.tell())
+            self.tag_v2._tag_data_limit = self._tag_data_remaining
             self.tag_v2.load(self.fp)
+            self._tag_data_remaining -= self.tag_v2._tag_data_size
             if self.tag_v2.next in self._frame_pos:
                 # This IFD has already been processed
                 # Declare this to be the end of the image
@@ -1273,6 +1301,7 @@ def _seek(self, frame: int) -> None:
                 self.is_animated = self.__next != 0
             self.__frame += 1
         self.fp.seek(self._frame_pos[frame])
+        self.tag_v2._tag_data_limit = self._tag_data_limits[frame]
         self.tag_v2.load(self.fp)
         if XMP in self.tag_v2:
             xmp = self.tag_v2[XMP]