Multiclassing between variants

[Rystil Arden]

I do allow that feat

Or at least, a more limited version of it (requires some ranks in Hide and Move Silently, and can only be taken a certain number of times).

Well, you're basically allowing it to be taken an unlimited number of times without the Hide and Move Silently reqs, plus a bit more, if you allow that multiclassing (which isn't to say you shouldn't, if you think this is okay).

The Sneak Attack fighter variant is very tricky though--you need to watch out for it in a bunch of combos (the simplest of which is the quick Arcane Trickster, where you go Rogue1/SAFighter1/Wizard5/ATX and you sneak into the PrC 1 level before you were supposed to get in)