How can 7 people play Rock Band 3 at once?

Seven people can play Rock Band 3 locally at the same time by going into All-Instruments Mode. This mode is also required in order to play with two guitars and a keyboard at the same time, even if you only want to use those three instruments. When in All-Instruments Mode, the vocalist(s) are not scored.

To enter All-Instruments Mode, hit "Start" on any of the instruments or the controller you are using for the microphones and check the box next to All-Instruments Mode.

If the game is asking you to enter All-Instrument Mode and you don't want to, it most likely means that you have three guitar/bass/keyboard dongles connected. You may need to unplug the dongle you aren't using in order to get the game to stop suggesting All-Instruments Mode.