Re-tiling the entryway to my home and had to remove the old mud floor that the old tile had been laid on top of. This lowered my floor by approximately 2" so now assume I need to raise by that much in order to place the new tile. My question is can I install multiple 1/2" or 3/4" plywood sheets on top of one another to build up my subfloor the additional 2"?
You can, but it's an expensive way to go, usually. And plywood is an inferior top surface for tiling onto.
If not simply re-doing the "mud" approach (worth considering - works well, may cost less) you could use (top down) 1/2" backer board (set on thinset), 3/4" plywood, and set the plywood on 3/4" strips spaced 6-12" or so apart, rather than two full sheets of 3/4" ply.