According to Fink, Vincent Bach advised against using overlapping mouthpieces as it would be detrimental to your embouchure. So does the reverse apply, could you successfully play Cornet and Bass with no ill effects? (Presuming you had sufficent time to practise both!) Or some other combination of instruments? I know because of contest rules against it, brass banders generally don't double, but this doesn't apply in the outside world. I recently had to do a "double take" when I saw a well known french horn player playing BBb Bass is a concert band!