Practicing hearing voices simultaneously

This is a post about improvising - I am wondering if anyone can help with this. I am a jazz pianist and I have been working a lot on pitching things internally and can pretty accurately hear the notes of a melodic line when i hear it. I also seem to be able to hear melodys internally and translate them onto the instrument. I can also hear (both internally and from recordings) a "sense" of the harmony and relate the melody to it (e.g. I can hear that the harmony is IV V I /whatever and generally the chord types). However I am having a problem with improvising and hearing more than one voice simultaneously internally and translating it to the instrument. I have practiced a lot of pitching melodies by singing, but how can you practice hearing more than one voice when you can only sing one at a time??!! I have practiced a lot of contrapuntal music like bach as i am told this is good for this, but still when I am improvising i find it impossible to hear in my head more than one voice. Perhaps my question is more about just hearing the multiple voices at the same time rather than figuring out what all the notes are. It's more a problem of not being able to picture more than one part at once.

Does anyone have any suggestions for this?