creating sub sites under a mapped domain on a Multi site

Hi I have created a Multi Site and have mapped a domain to the multi site platform now what I want to know is it possible to create sub sites on a mapped domain such as and have the domain act like a independent site from with its own theme and plugins and it would be all running on the Multi Site

also only allowing the owner of to create a new site under the domain

not sure if this made any sense however this is how I see it working