Basic Action Super Heroes!

If a character possesses both of these and doesn't move or activate anything, can they get 4 attacks with a -2 dice penalty?

That's how I do it. I think that it has to be with "normal" guns though, not with powers.

Technically, I don't think so, since Double Tap says "you cannot move or use any other powers", and Offhand Shooting is another power.

I'm not sure I think it would be all that unbalancing to allow it, though. For example, if you don't need to stick within the limits of an Intense Training power for some reason (to qualify for Normal, or whatever), you could just spend 2 points to get Super Speed 3 with a limit of "usable only for ranged attack panels", plus Offhand Shooting for 2 points. It costs 4 pts instead of 3, but doesn't limit your mobility or other power usage. Heck, to make it "identical" you could apply a limitation on your Offhand Shooting that you cannot use that while moving, to end up with a 3 pt combination that is basically the same thing.

EDIT: Ninja'ed by the Bashman...