Here's how you can have multiple versions of beat saber at the same time by having different package names.
Unfortunately, BMBF is hardcoded to use original BeatSaber package id, so it's not possible to have completely unmodded version with BMBF modded version.
If BMBF starts using this method, it would be possible to have unmodded beat saber from oculus store with multiplayer support and modded BMBF version.
I made this because BMBF modded version used to crash time to time, and I prefer to have choice between stable game and custom songs.
You'd need apktool, zipalign, apksigner – I'm on mac, so I've installed apktool from brew and used Docker for other tools: fopina/dedroid.
Grab the APK