It's been gnawing on my brain for the past 20 years... I love Scifi/Fantasy books and pretty much read all of Isaac Asimov and Piers Anthony books. I hope the collective SciFi mind can help me out:
The premise of the books is that the humans have colonized the galaxy. Humanity was, however, broken up into 3 factions. The Chinese, Americans and Russians (I think) ended up as the primary groups. Each group has its own sectors of the galaxy, and there is a lot of distrust and there are skirmishes (I'm not sure if they were at war).
During this time there were people with mutant powers. Powers such as telepathy and telekinesis. There were also people who were Null (not affected by telepathic powers). I also remember that individuals had tattoos or markings that signify, either their faction or their powers (I'm not sure)
The whole story is that each faction had a military group or squad after SOMETHING in a tower/building. The book would jump from the perspective of faction to faction to tell the story. Each faction, had a protagonist and would have their own storyline. There was one part where 2 of the factions had a firefight: faction A detected that faction B had a telepath scanning their tactics. When the Null person found out, she (I remember that she was a she) changed the settings of the blasters of her fellow soldiers to a stun/spread mode. So when they opened fire, they where able to hit several Faction B people and either advance or retreat to the tower/building.
I kind of remember that the book title had the word "Three" in it. Somehow I thought it went along the lines of "The Three Towers". Also the cover was a 70's dark color theme with a soldier looking towards a tower or building.