Yeah I've done all sorts of combinations of beer/liquor in every order imaginable, and I very rarely get sick or have a hangover the next day. It usually depends more on the sheer quantity of what you drink, though I do know some people that can't take on type of alcohol or the other for some reason.
And there is absolutely no problem with having two kinds of beer in one night. You can even have two kinds in one drink if you'd like (e.g. black and tan, snakebite, etc.).