Multisite, but register locally?

I have multisite set up and am using it to power several sites. The sites are not necessarily related to one another, and it’s very confusing for users when they’re redirected back to the network “root” to register and confirm.

Is there a way to register/confirm/etc locally on the child site (or at least make it appear that way) to avoid confusion? I want it to appear like they’ve never left the child site.

I greatly appreciate any help or suggestions you can offer.