Moving many pieces at once is certainly one way of fudging with the chess formula.
Attempting to redesign chess is a pretty old idea, and happens fairly often. But not often enough, I think. Apparently the people who made Regimental Chess agree with me, and have just put their video game component in beta for mac and PC. Regimental Chess has two primary conceits: If multiple pieces can move similarly, then those pieces can move simultaneously in formation; If you have more than one army, each army can move its pieces each turn. From there, the game blows up into an interplay of brutal and dynamic tactics.
The game, fascinatingly enough, forms a rock-paper-scissors style meta competition. Kings are best protected from fast formations of queens and bishops by knights, but knights are very vulnerable to formations of pawns. Those same pawns are quite vulnerable to the aforementioned queens and rooks.
It gets pretty crazy from there.
If you're interested in more information, or you'd like to try out their free beta, you can go to the Regimental Chess website.