obviously, if the input signal is driving both "sides" in phase, you will get canceling at the output side, and a lot of heat... I take it you are thinking of a waveform like 120Hz full wave rectification from 60 hz.? otoh, if you are thinking like square waves, as in digital, it seem to me that you'd have to shorten up the duty cycle to fit the out of phase component inbetween the inphase component in order to make the frequency double... or so it seems to me...
Interesting idea... seems to me that IF you can make this "alternating doubling" work, you make two halfs, each doing the doubling, then run those two halfs (each one then an altered P-P stage) into a PP output to kill the second harmonic as before. More or less a sort of bridged amplifier I suppose...
Might work out to be "band switchable" between any two bands?
_-_-bear