Having a big stack doesn't exempt you from pot
odds and probabilities, if you start chasing draws regardless of the odds you're getting then you're going to go broke in the long run. You should always be asking yourself what your opponent could have that beats you, losing showdowns when you should have folded much earlier will make your stack shrink pretty fast.
What you can do is use position to your advantage and 3-bet more, even if you can't call a 4-bet you will start to create a table atmosphere where people will be afraid to bet because they don't want to get raised. You want to be the aggressor, and only follow along if you are getting good odds or have the stone cold nuts and are giving your opponents rope to hang themselves with.