How to change Box "metaphisic" orientation

As the title says, is there a way to remap/edit the orientation of a box? I guess it depends on a plane or point... Somehow trying to reorganize its own values (UVW) whitout changing the geometry.

The situation is that during a box morphing the pieces are not well oriented (I can not change the original piece orientation because it goes to many boxes, some are well oriented and others are not). I can either orient the targets boxes or results because the boxes are not regulars (for regular I mean X=Y=Z), and so, larger and smaller parts would swap.

So, somehow I would need to know the vector or plane that defines de orientation of the target boxes and change it by ones defined by me. 

I hope explanation is clear enough.... Thanks a lot in advance. :-)