I think laser (lazer?) tag should work like this, based off what I find fun in real life.
1. You shoot people. Their gun is disabled for 5-10 seconds, and they can't be hit until it starts working again. You gain points from this.
2. You shoot enemy targets. This gains you points.
3. Enemies shoot your targets. You have to, obviously, hit them before they can shoot the target.
Works out perfectly for teams.