Some of the hands that flat the initial raise should be strong enough to withstand a squeeze, either when the original raiser folds, or when he calls and you overcall.
e.g. In the this spot, MP opens 2.25x, hero flats (JJ) in CO, BB squeezes with a PSR, MP calls. CO should overcall, because JJ will be profitable multiway in position.
It should also be profitable in this spot to overcall QQ (if you didn't 3-bet pre), AQs, maybe TT and probably some small SCs (76s, 65s, 54s) too. AQo, AJs, KTs, QJs, JTs and even 99/88 might be slight losers as overcalls. If your initial flatting range is much wider, then you are indeed vulnerable to squeezes, which is why (in tough games) you shouldn't do much cold-calling pre-flop in the first place, as you'll have to fold to squeezes so often. Note also that if the squeezer makes a larger raise than pot, your odds will be worse and you have to fold to the squeeze more often.
If the squeezer has position on you, then it really sucks. If BTN had squeezed vs MP+CO in my example, and MP flats the 3-bet, I think even jacks have to fold, as it will be so hard to control the pot-size/get to showdown OOP to the squeezer. Your flatting range would be so capped and face up in that spot (looking like QQ-TT) that BTN should be able to play perfectly against you.