Here's a brief excerpt of a drill from the third day of a 4-day rifle training class from Suarez International. In this drill, a teammate and I are advancing on a position while maintaining covering/suppressive fire. To do this, one of us keeps fire on the target area while the other moves a short distance forward. Roles then switch, and the second team member moves up while the first provides covering fire.
The key to this is communication, and the purpose here was really to practice communicating with your partner. I should also point out that as we were continuously moving downrange of each other, we were completely violating normal range safety protocols. This was not a safety issue because our movement routes kept us each well away from fire and because we were both competent shooters who were not going to start throwing wild rounds all over the place. In addition, to actually practice real-world combat use of a rifle one must eventually move beyond the square range paradigm.
Interested in taking a class like this yourself? You can see Suarez International's couse list and calendar here: http://www.suarezinternational.com