ORIGINAL: MinnFlyer
It won't be possible to drill new holes so close to the old ones.
Depends upon the mount and distance.
Someone here posted a great solution for aluminum mounts, where you can friction weld a plug using nothing more than a tap & die set, a piece of aluminum stock and a drill.
They suggested putting threads on the stock and using the drill to screw it into place at high speed until it breaks off... effectively friction welding the aluminum plug in place.
Apparently you can then redrill the mount after this is done with no ill effects.