How do you deal with sneak attack if you multi-class in classes with sneak attack? I understand that for now the rogue is the only class with sneak attack, but i we're using 3rd party and home brew and I'd like to know how to deal with it.
Since you're using homebrew, the only way to deal with it, is through more homebrew. The option you pick is entirely within the realm of your own game, though.
Looking at previous editions, it used to be that Sneak Attack would stack from various sources. You could still do that.
In 5e, the only ability that explicitly stacks is spellcasting spellslots, where you add together levels of classes that give Spellcasting; you could do the same with Sneak Attack if you want.
You could also wonder what purpose a second class with Sneak Attack has, and whether it shouldn't just be another Rogue subclass.
Whichever option you pick; you're on your own. New classes for 5e come out very sporadically, and I doubt there'll be any others that have Sneak Attack in the foreseeable future.
5e RAW can't help you
As you correctly state Rogue is the only 5e class that has the sneak attack feature. Therefore the correct answer is entirely up to your DM.
However, if you look at previous editions which did have multiple sneak attack classes you may find a solution.
In pathfinder sneak attack stacks
This is exactly like the rogue ability of the same name. The extra damage dealt increases by +1d6 every other level (1st, 3rd, 5th, 7th, and 9th). If an assassin gets a sneak attack bonus from another source, the bonuses on damage stack.
Similarly in the rules for monster advancement:
If the creature possesses class features (such as spellcasting or sneak attack) for the class that is being added, these abilities stack. This functions just like adding class levels to a character without racial Hit Dice.
I would suggest you use a table similar to the Multiclass Spellcaster which allows identical class features to stack.