Use two ADC channels to increase resolution
This is a very good idea. The BioTac tactile sensors from Syntouch do this very same thing. They have a pressure sensor inside them which captures both the low frequency part of the signal at about 50 sps, and the high frequency components amplified and sampled at 2000 sps. This works beautifully.

However, I don't know if you can actually combine these two signals to create a higher resolution, I.E. more bits. You may be able to with some clever signal processing, but it wouldn't be trivial.

Another way to increase the ADC resolution is by oversampling. If you take 16 12-bit samples (and assuming there's at least one LSB of noise) then you really have increased the effective resolution.