Based on your updated requirements, a custom design with far more specifications including CMRR, Gain, Nyquist filter, electrode probes, motion restraints , ESD protection and cabling specs are needed to pickup the uV level signals with > 40dB SNR and amplify to TBD output levels for a suitable MUX and ADC.
So rather supplying a commercial solution or suggesting this much broader question than the scope of this forum to be deleted, I suggest you examine commercial solutions that have solved all these requirements and ask yourself, how did they do it?
BTW a range of 2⋅10^3 needs 2^11 range or >=11 bits
There are many commercial solutions to this problem, so your problem is a good one, yet disliked by many moderators of this forum. It is a fizzy question that is solved by experience using a low cost ( yet ugly) portable EEG scalp monitoring system that can combine many hardware channels with very high gain, high impedance and very high common mode noise rejection ratio with customizable analog filters, digital filters and a wireless 32 channel mobile computer with a host that performs the fuzzy logic learning. Once the algorithms have been optimized for one person with a trans-cranial electrical stimulation people with this affliction can be treated in future. I would imagine a self-contained system under a wig or a tight fitting toque with the hardware and interface to a smart phone.
- wired scalp with wireless sender to host CPU/GPU