Need Help - Experiencing different TRPG while continuing a storyline through them

I've been interested to DM a game where the player would play different character while trying different systems at the same time. Every few weeks, we would be switching system and when doing so, the setting would change as well (Sci-fi, medieval fantasy, Grimdark 40k i dunno these are example). The only thing i'm a bit puzzled is how to make it work.

I'm sure it won't be an easy task but how should i make it so the player keep a certain level of progression while switching system without sticking to one system for the classes and level? Just not looking for a hard reset every time they switched system.

My idea is a sort of multi dimensional game in order to explain these change in the settings (and systems) btw, if it helps.