The Chinese also use baiji (白芨) which is the root of an orchid, also used in Chinese medicine and as a natural glue (to make silk strings for musical instruments like the guqin etc); the glue is released by boiling the roots. It had been used during the mounting process in the past but not any more as I think it turns paintings yellow-brown over time, hence why many Song/Ming Dynasty paintings etc are really brown. It’s like how varnish turns old oil paintings brown after many centuries.
Hide glue (明膠) is mainly used to bind pigments together and I wouldn’t use it for mounting as the wheat starch paste is sufficient.
Alum is not much of an adhesive as it is a preserver and waterproofer and has insect repellent properties, so a pinch of it is added to the paste mix.