A lot here depends on what you call "Frame". "If" you are including the Standing Breech in you definition of frame the answer is a resounding No. Stocks & forend irons may well interchange but barrels won't. A 12ga has a taller & wider breech than does a 20 say as well as having wider spaced firing pins.
Personally if the body & bar are the same with only the breech adapted to a different size set of barrels I do not call this a different Frame, but many do. I guess you could say I agree with John E, but just want to say the barrels will not normally fit from a different gauge or even weight of gun.
