I think you'd be better off to amplify the signal, rather than try for a higher resolution A/D.
Suppose you have a 10 bit A/D, with an input range of 0-10 volts. Ten bits is 2^10, or 1024 ~ 1000 possible numbers. So this A/D can resolve signal
differences of about 1/1000 of 10 volts, or 10 mV. If you have a 10 mV signal, you can "see" 0's and 1's. But if you amplify that signal by, say,
100 x, then it will be ranging from 0 to 1 V, and you'll have better resolution.
You get the best performance, resolution-wise, if the signal matches the input range of the A/D.
It isn't terribly hard to build a 100X amplifier from op-amps. I've built 1000x amps as well, but usually had noise problems.
Good luck.
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