I love these types of puzzle games, where you can invert the colors to find new paths for a level. For a multiplayer game it seems it would become frustrating, unless you put a limit on the 'changing effect'. How do you change it, key press or switch in the level? You could get into 'changing' wars with other players it seems. Maybe have it timed, or have a switch in the level to do so, put once it 'changes' the switch it unavailable and a new one appears.
Just something to think about to keep the game fair. Looks cool non the less.