Biggest Caliber?
In my mis-spent youth I did carry a four inch .44 Magnum, model 29 S&W. In a pancake holster it fit rather well under most any decent jacket.
In terms of actual bore diameter, I've used a single action Peacemaker replica with a bore diameter of either .452" or .454", I've never been sure.
For any sort of 'walking around' gun, either concealed or open, .44 Magnum is probably the biggest (horsepower) handgun practical. Frankly, if I think I need something bigger, it'll be either a shotgun or rifle.
If that doesn't answer your question, let me know and I'll confuse you further.