No one can answer this question for you, try a whey shake and see how your stomach feels.
I certainly wouldn't suggest suddenly adding 6 shakes to your diet off the blocks. Why would you jump into it like that.
I have 4/5 shakes a day and I think that's almost overdoing it. 6 seems excessive, but each to their own.
Anyway, try adding in a shake post workout, and if you have no stomach issues add another before each training session and progress like that. If you do have stomach issues with whey, then try a different form of protein powder if you really want to use protein shakes (egg protein etc)