Complicated Scenario with Membership Plugin

Hello to the team!

I would some help about a scenario. Here it is:

I have a multisite with the membership plugin. The members can register through the main site. Then I would like to add every user to a new blog with a specific user role which is the same when Memebership plugin give it to him at the registration process.

My question is, if the membership expires and the member doesn't pay, how can I restrict the access to the blog he is also a user.

With some test I did, I saw that if I disabled him through Membership (or move to a no subscription plan), he cannot log in into the main site but he can login in the blog.

I would like to restrict his access everywhere in the network!

How can I do it?