| Caveat: I am not a luthier.
But I had some damage to the inside layer of a plate from my Kay when I opened it up in 1982. The damage was such that I could not simply glue it back together.
Purchased for some long-forgotten project, we had some maple veneer that was magically the exact thickness needed. It is somewhere around 1/32 inch thick, which I think is a standard thickness.
I had to clean up the jagged edges of the first layer on the plate, then cut pieces of veneer to fit. Then I got the veneer flexible (soaking or steaming, I can't remember), did the final fitting, and glued them down. I clamped between boards with pads made from 3/4 inch thick styrofoam insulation, which crushed slightly to take the curved shape.
As is my habit with anything tricky, I practiced all of these operations "dry" before committing to glue.
This repair has held up since it was done. Obviously, what I can't tell you is perhaps the most important part: How to make the seams invisible and match the finish. That's a matter of luthier-craft which is beyond my knowledge and skill. At the time my main concern was mechanical integrity. | 
