I don't have that set up, but it should be doable. I would just be sure that the doors open the same direction, and that you get a freestanding microwave, not some kind of built-in. Be sure to leave a few inches on each side of the microwave for venting and to be sure that the micro door can swing open freely.

I've seen cabinets that house microwaves with a garage lift style door as well as pocket doors. Check with you cabinet designer.

Definitely possible, that's what we did!

Doors open:

Doors closed:

Here are pictures or ours with the garage style door opened and closed. The cabinet is 18 inches deep and is recessed into the wall 3 inches.

ours is in an upper corner cabinet:

I have keenly wanted this, but am working with existing upper cabinetry that is only 14" deep and due to ancient studs cannot recess. Am tearing my hair trying to find a decently-powered microwave to fit.

If you go this route, I strongly advise recessing the shelf into the wall and making the upper as deep as possible, since only a very few microwave models will fit a cabinet shallower than 15 or 16" leaving enough room for a door.