Different jurisdictions have different policies. You'll want to check with whoever issues permits in your area and be prepared with drawings of the proposed project, especially any demolition or structural aspects.
You may only need to have the electrician get a permit for his/her work and the plumber another, though if you are adding one or more bedrooms, it can be decidedly more involved.

I don't believe many municipalities are going to issue multi-year permits for something like a basement, although as Randy suggested you may be able to break it into the various stages.

Talk to your build code folks and see what they have to say.