For Bach fugues I do this. First I write out the fugue by hand with each voice on a separate staff. That in itself is helpful, because all the sudden you can easily see all the fugal entrances and fugal devices like augmentation or inversion. Then I listen to a recording of the fugue many times, each time using my written out version to help me follow just one voice. Then I do the same, singing along with each voice. Then I play each voice separately on the piano. By that point I can really hear each voice clearly and I know them well. Then I learn the fingerings, hands separate, and practice hands separate trying to keep the distinction between voices when there is more than one in a hand. Then I put hands together. The copying out does take some time, but since it takes me a long time to learn a fugue anyway, the time required for copying it out and listening voice by voice is pretty short compared with the weeks I'll be working on learning the fugue anyway; and I think it makes the whole process quicker in the long run.
Apologies for quoting the whole post -- it's good, though, and I agree. I've only played one fugue, back when I was a kid, without either making or finding an open score.
As a practice technique, I also find it's effective to, once you have the open score, just play a few of the voices all the way through, ideally with the fingerings you'd use, but maybe not if you just are interested in studying the fugue or are truly memorizing each voice for singing in a mental-practice stage. It kind of gives your ego a little boost if you can play a supposedly difficult fugue at a desirable tempo, even if it's missing a few voices.
That said, I wonder just what the limit is to truly hearing many voices polyphonically. I know some people are better than others, whether through practice or some neurological patterns originating elsewhere, but surely there must be some kind of hard limit. I doubt there is an answer, so until then, I'll go on like everybody else and keep trying to improve.