You will probably trade accuracy for speed, and you can
expect some trouble measuring accuracy at speed on the
bench or ATE.
A plurality of high bandwidth low gain stages will work
better than a single or few high gain high impedance
stages. Though this can be prone to internal crosstalk
and oscillation at low input difference.
You are in a race between gm*Ro (gain) and Ro*Co
(bandwith) at every stage.