If I understand correctly your question, that's something that you can do with CB Auto Actions add-on, as follows:

E.g. Add an auto-action as follows:
- Triggered by onBeforeAddConnection and/or onBeforeAddConnectionRequest
- Type: Redirect
- Condition: Field "Connections" is "Greater Than or Equal to" "3"
- Action: URL: Homepage (e.g. "/" or "/homepagesubfolder"), Message: (e.g.: "NOT ALLOWED MORE THAN 3 ACTIVE CONNECTION, you already have [Connections] connections."

This will be limiting connection requests, once 3 active connections are accepted and established, but it does not limit connection requests before they are accepted. For that, probably some more sophisticated auto-actions would be needed.

Does that address your question ? If not, please clarify the question, so that we can try to address it.

P.S. Moving your topic to professional forum for priority support, as you have the corresponding membership.