I've made all sorts of things with reinforced panels -- it's easier to attach the lumber to the panel than it is to build a frame and hang the panel from it.
Cut out sheet goods (MDF, plywood, whatever).
Cut lumber (1x2, 2x2, whatever)
Screw (and/or Glue and Screw) the lumber to the edges of the panels). Screw the reinforced panels together.
If I make a box, there is only one reinforcement stick per corner.
Hope that makes sense.
Bob