There are *loads* of studies / PhDs / monographs that are based on only one case-study. I'll cite you just one example: Working for Ford by Huw Beynon. I'm sure this is covered in core business research textbooks (Bryman & Bell, Easterby-Smith etc.). But as a general rule, if you offer less depth, you need to offer more depth.
Regarding research methods, will you be looking to use other research methods? Primary documentary analysis? Secondary documentary analysis too? All this will add richness and depth to your case-studies.
I'm assuming there's a reason why you won't be going to your chosen country.
Just as a little aside, as a post-graduate forum rather than a lecturer's forum, I'm guessing most people on here aren't doctors yet.