aiohttp.ChunkedClientResponse currently treats the first chunk's size as the size of the full data (chunked encoding is specifically intended for situations where the full size isn't known when the transfer starts) and there is only a single chunk.

I don't think that's correct. The current code does support multiple chunks, using the self.chunk_size variable to keep track of how much is remaining in the current chunk. When that becomes 0 then it reads in the next chunk header and start the process again.

This allows you to read in a chunked response in separate chunks, where the chunk sizes are different. Eg the incoming data could be chunked every 256 bytes, but the application reads in 16 byte blocks:

resp = session.get(...)
while True:
    data = await resp.read(16)
    if not data:
        # end of stream
        break
    process_data(data)

IMO that's a useful extension to standard aiohttp because most microcontroller applications can't read in megabytes at once.

I think the only issue to solve here is handling -1 to indicate that you want to read everything.