I think there are a couple ways you could set this up.
There's networks - So, you could create a network for your group, or a network for specific sub-sections of your team: Marketing, Finance, etc.
There's Projects - You could set up a Marketing Project, A Finance Project, and a General Project (Granting only those who need access to that project)
Or you could use tags - as a way to categorize tasks that live in a single project, but, include a couple different groups - ie, rolling out a new website would have tasks for Finance, Marketing, and Others.
Happy it discuss it through, with you.
Producteev & Jive