Feeding a signal directly to an ADC or amplifying (active) it beforehand?
Don't dink with it.  TI has a pretty good grasp of what they are doing.
Specifically:

Don't add a DC blocking capacitor.   The ADS1299 implements &quot;Lead Off Detection&quot;  (see section 9.3.2.4.3 in the datasheet) to tell you when the EEG leads are not making good contact.  That relies on DC coupling.  Your blocking capacitor would also block the lead off detection.
Don't add additional amplification.  The ADS2199 has programmable gain amplifiers built in - you'd be duplicating that function.  Amplification of microvolt level signals is harder than you expect - your additional amplification may well add more noise and offest than the benefits you (might) gain from more gain.
Don't add additional amplification. The amplifiers would interefere with the lead off detection.  The lead off detection would always &quot;see&quot; a good connection through the amplifiers - or maybe never &quot;see&quot; a good connection through the amplifiers.

The &quot;ADC&quot; isn't merely an ADC.  It is a system intended for a specific use, and includes functions beyond just converting analog signals to digital.  Unless you have  good grasp of what it is doing, it is unlikely that you'll be able to improve on it.  Even if you know what you are doing, implementing an improvement to the ADS1299 won't be trivial.