What I’ve started doing is have classes with good saves give you Great Fortitude, Iron Will, and/or Lightning Reflexes as bonus feats at 1st, instead of starting at a +2 base saving throw. That way, they don't stack when multiclassing, plus you avoid some of the stupidest feat taxes in the game.
Many other DMs just have the base +2 not stack, so you can only get it once per save. I think using the feats is better, though.
And in all cases, fractional BAB and saving throws are used, because not doing so is nonsense. When you use fractional (and block the +2 stacking for saves), you end up with multiclass characters whose base values are the same as single-class characters. When you don’t, you wind up with multiclass characters with inappropriately low (or high, if you don’t block the +2’s) base stats for no good reason. It introduces an awkward, artificial “breakpoint” in multiclassing that adds no value to the game, or results in uncomfortable character skew if it goes ignored.
As for allowing the +2 only from your 1st-level class, that I don’t like at all—every time something depends on the order in which you took your classes, you significantly complicate the game. It also leads to incentives to metagame, or “punishments” for not doing so, which is the opposite of how the incentive structure should work.