Can a child site have its own membership?

Hi there

I wonder whether if a child site can have its own membership.

What I exactly meant by that is

people sign up for a certain child site and they are only granted access to that particular child site.

I am currently working on a site builder service.

The people sign up for the solution (on main site) and they are given a site (child site).

I wish to install a membership plugin on a child site so that the user can have their own membership system.

I have seen some membership plugins, however they just allows users to create child sites upon registration on the main site.

Your help will be much appreciated ??

Thanks in advance