Private site in Multi site


I want to lock down a whole site within a multi-site e.g. a family only site

The plugin 'members only' and 'absolute privacy' would do the job except neither work in a multi site context.

With membership, it appears to me to hide content but not the whole site, all I would want visible to non logged in users is a login page.

Is there any way to achieve this with 'membership'?