To add to the depth, I'd just start from scratch.

If it's just a mirrored door attached to a shallow box via hinges, and if you really like the mirror and frame because its curved/bevelled/both, then buy it and have a deeper box made for it. That will definitely be cost effective, because curves and bevels cost more to make one at a time than in quantity.
Casey

It might come out a wash, and if you have a door you like (or want) may be cheaper to build a new 'box'.

Buy the time you purchase hinges, a mirror, a latch, etc the door from a purchased unit might be cheaper.
As noted above if you have a special door you want to use just build a new box.