It is possible to have multiple menu items to point to a single page in the system. If you manually enter the full URL (instead of just linking to the page which constructs the URL internally) then it is possible to pass in a querystring value to the page as well. There is no need to create anything other than a generic Module. The module instance on a page is controlled by the Portal framework.
Once you have defined your module (a module is always defined as the executeable code and user controls) you may add it to a single page and use the technique described above to handle multiple teams. It is then up to your module to handle keeping each teams data properly separated. The better approach is to have your module focus on keeping track of a single team and then just create multiple pages where you place a new module instance on each page. This is probably the easiest way to go and is the most flexible. With the second approach you would be able to customize each team's page to include custom graphics and also maybe an ad from the team sponsor.
Joe Brinkman