diff --git a/openml/runs/run.py b/openml/runs/run.py
index 945264131..f39ec1f3c 100644
--- a/openml/runs/run.py
+++ b/openml/runs/run.py
@@ -6,6 +6,7 @@
 from collections import OrderedDict
 from pathlib import Path
 from typing import (
+    IO,
     TYPE_CHECKING,
     Any,
     Callable,
@@ -149,6 +150,7 @@ def __init__(  # noqa: PLR0913
         self.predictions_url = predictions_url
         self.description_text = description_text
         self.run_details = run_details
+        self._additional_files: dict[str, tuple[str, bytes]] = {}
         self._predictions = None
 
     @property
@@ -614,6 +616,35 @@ def _parse_publish_response(self, xml_response: dict) -> None:
         """Parse the id from the xml_response and assign it to self."""
         self.run_id = int(xml_response["oml:upload_run"]["oml:run_id"])
 
+    def add_file(
+        self,
+        file_name: str,
+        content: str | bytes | Path | IO[bytes],
+    ) -> None:
+        """Attach additional file to this run.
+
+        Parameters
+        ----------
+        file_name : str
+            Name under which the file will be stored on OpenML,
+            e.g. "model.onnx" or "weights.bin".
+        content : {str, bytes, pathlib.Path, file-like}
+            The file content. If a Path or file object is passed,
+            it will be read into memory and stored as bytes.
+        """
+        if isinstance(content, Path):
+            with content.open("rb") as f:
+                content_bytes = f.read()
+        elif hasattr(content, "read"):  # file-like
+            content_bytes = content.read()
+        elif isinstance(content, str):
+            content_bytes = content.encode("utf-8")
+        else:
+            content_bytes = content
+
+        # store as (file_name, content) tuple
+        self._additional_files[file_name] = (file_name, content_bytes)
+
     def _get_file_elements(self) -> dict:
         """Get file_elements to upload to the server.
 
@@ -644,7 +675,9 @@ def _get_file_elements(self) -> dict:
                 self.model,
             )
 
-        file_elements = {"description": ("description.xml", self._to_xml())}
+        file_elements: dict[str, tuple[str, str | bytes]] = {
+            "description": ("description.xml", self._to_xml())
+        }
 
         if self.error_message is None:
             predictions = arff.dumps(self._generate_arff_dict())
@@ -653,6 +686,10 @@ def _get_file_elements(self) -> dict:
         if self.trace is not None:
             trace_arff = arff.dumps(self.trace.trace_to_arff())
             file_elements["trace"] = ("trace.arff", trace_arff)
+
+        for key, (stored_name, content) in self._additional_files.items():
+            file_elements[key] = (stored_name, content)
+
         return file_elements
 
     def _to_dict(self) -> dict[str, dict]:  # noqa: PLR0912, C901