Ok, now I'm not really sure how you would have a ceiling outdoors, but in reality, this is the idea that I think you are trying to accomplish.
You want to use mirrors to reflect the background and the ceiling's black and white patterns, along with your subject?
Ok, can you do this outdoors? Yes you can, but realize that you're going to need to go heavy on the reflectors, and they will need to be large enough to cover the area of the background and celing. So you'll need to invest in those just as much as you would lighting on the indoors. Hypothetically, that could be much trickier, too, because your light source will be moving. (The sun.)
Indoors would be easier, and you would want to run the set as if it were a high key studio, and use your subject accordingly. Everything will have to be super clean, no lint, dirt, scratches, etc. You will need your ceiling and lights lit on their own, so that shadows dont fall. You'll need to make sure that any flashes you have that hit that mirror dont create reflections of light on another part of the photograph. You'll want to try to avoid any direct lighting to the mirror, and instead have the lighting on the subject and background.