Raad, you're right; I don't think you can do dotLRN subsites.
Although it would be possible (as far as I know) to run multiple sites that use the same data, it still wouldn't really do what you want, because all of a student's courses would be visible in each one (meaning that in each site, most of the courses would look "wrong"). And the more they looked like different sites, the more you would have users who were surprised that a customization they made on one site showed up on the others.
What is really needed is the ability to set theme by class/community, but that feature doesn't currently exist.
