I have two french doors, each with an overlapping tongue. The doors are interior doors, so there is not one side or the other that particularly needs to latch. They need to be able to be opened from either side.

Because of the overlapping tongue, a standard inset and flush mortise lock set will not work. Does a mortise lock set exist that can be inset into one of the doors that has an L-shape to it and a catch that is also L shaped to accommodate the overlaps?