Yes. It's very possible. We've done it successfully for clients.

However, what we tend to find is that once we get started all sorts of ways in which the sites need to be different start to emerge and the process becomes much more complicated than it first sounds, and needing of a high degree of technical competence to make it work.

For starters though, you'll need to adjust your base installation to tweak the store-side configure.php file to recognise and perpetuate the different domain names.

Then you'll need tweak the init system to display the appropriate template for each domain.

And you'll also need a multidomain SSL certificate to allow each "store" to have a properly encrypted checkout.