Do you need multiple instrumental amplifiers and filters for multichannel EEG systems?
You can of course use a single amplifier for all your signal of a single channel, if you apply your band-filters afterwards. You'd need to model where in your device noise appears to see whether that has any downsides.

You of course can't amplify different channels coming from different sensors with the same amplifier. How would you separate two signals that you've added up?

Also, "multiple active filters" very much sounds like a design anachronism: We've had computers fast enough to process EEG signals for about 40 years now. A bank of filters can very well be implemented in software – and it's way easier than building a bank of analog active filters. All you'd need is an analog anti-aliasing filter, so that you can throw an ADC at your analog signal, for example a soundcard.