change theme on multi site

I am building a site. Basically the site will have multiple components to it. Each component will exist of multiple pages.
I want to use the athaulapa theme for some of the components. the theme has to be editable for each component without affecting the other components using the same theme.

i was considering installing bitnami untill i read that changes made in the theme for one component changes the theme for the other components.

Is what i am looking for possible ?

Thanks