Storage Bench Possible with 3/4" Plywood/MDF?
ideas to make it stronger

Resisting vertical forces
Add a rail front and rear, inset from front and rear edges. The rail would be 31&quot; wide x 2&quot; high. Make it taller for greater strength.
Resisting lateral forces
The greatest weakness is lateral collapse by lozenging. Adding metal corner brackets or adding a back panel would prevent that. With an inset back panel you wouldn't need a rear rail.
Minimum would be an unobtrusive triangular wooden brace centrally at each end of the underside of the top, glued with tenons or plenty of dowels.