Repairing streamed HTTP chunks in Haskell conduit

Question

I'm streaming chess PGNs from the Lichess API. Streaming is recommended, since any given user could have up to ~500,000 games stored. The goal is to parse the PGNs in a parsePGNStream conduit as they're coming in. Unfortunately, the stream chunking is arbitrary and PGN-agnostic -- meaning there has to be some kind of intermediary conduit which concatenates chunks so that each piece of input is a complete PGN ByteString once it reaches parsePGNStream.

reqBr GET (url) NoReqBody opts $ \r -> do
      runConduitRes $ (responseBodySource r .| repairChunk .| parsePGNStream .| BS.sinkFile "./test.pgn")

I have a partial PGN parser which recursively finds the first complete PGN-match in a given ByteString

stepParse i
  | valid = Just i
  | BS.null i = Nothing
  | otherwise = stepParse (BS.init i)
    where
      r = MP.parseMaybe pgn i
      valid = isJust r

If I had to guess, the solution probably involves some kind leftover which feeds unconsumed input back to the conduit input -- but everything I do seems to be a dead end. How would one go about implementing this?