It can certainly be done, but you'll have to attach wood under the current cubby holes, then build that up to support the seat extension. That support piece should be at least 8" deep. With about 2" to 3" sticking out past the cubby hole. Does that make sense?
The other alternative, that might look more purposeful, would be to make a 4" or so seat extension. Hinge it to the existing seat, so that it can fold down when not needed. You can make triangular support pieces that are also hinged, and would fold out from the sides of the cubby holes to support the seat when upright. Fold them back in and the seat extension folds down. You loose a little bit of cubby space while it's folded, but none when it's extended.