Subscription based on Groups.

We would like to offer a free membership ($0.00 per-month subscription) to all visitors.
Once subscribed, members can add one or more Groups (communities) as needed.
We plan to charge a monthly fee for each community created. 
Please advise how we can implement this. 

I assume by groups you mean CB GroupJive Groups? By add do you mean create groups or join groups? There are no join limits in GJ. It is possible to limit group creation though and it can be based off a field so you could adjust that field using CBSubs Fields integration for paid group create limits. This can be configured in CB GroupJive > Parameters > Groups > General via the "Create Limit" parameter.

Yes. I mean GroupJive Groups.
By 'add' I mean the ability to create and moderate a group. {All users can join a group}
Can CB-Subs allow the upgrade and configure GroupJive in the backend?

Yes that's doable then. All you need to do is create an integer field in CB > Field Management. Lets name it cb_grouplimit for example. Next in CB GroupJive > Parameters > Groups > General set "Create Limit" to cb_grouplimit. Now in CBSubs using CBSubs Fields integration configure your plans to increment or set the value of cb_grouplimit as needed. So for example if a subscription gives 10 groups then you would set cb_grouplimit to 10 on active subscription. This gives you paid group creation limits.

I tested the "CB GroupJive > Parameters > Groups > General" option by setting  "Create Limit" of zero to integer field cb_grouplimit.
It does not work when value cb_grouplimit field is '0', as the user can still create a Group.
It works fine when the value of cb_grouplimit is '1' . In this case the CB allows only one Group and then the option "+Create New Group" does not display anymore. 
Seems like the logic is ignoring value of '0'. 

Please advise. 

A create limit of 0 is unlimited. To disable creating entirely you need to use access controls. The easiest way to do that is give them a usergroup when they subscribe and take the usergroup away when they expire. That's configured under the Access tab of your plans. Next create a View Access Level that includes this new usergroup and any other usergroups you want to have group create permission. Now set the "Create Access" parameter to that new view access level.