This is what Trello organizations are designed for. An org is a collection of boards and a group of people, with permission control.

This is Fog Creek's org: https://trello.com/fogcreek

You'll just see our public boards, but we also have boards that are visible only to org members. Granting or restricting access to all of them is as simple as adding or removing a user. You can create and be a member of as many orgs as you want.