I've not heard of re-submitting an already certified building other than pursuing EBOM. For starters, you may want to go to LEED online v3 and go thru the "Register a new project" steps - if you choose the option that helps select a rating system you'll get a series of "wizard" screens with questions on the extent of the work scope that may help answer your question. Make sure you follow the "more..." links for additional tables.

If the new work is extensive enough to count as a "major renovation," it would probably mean pursuing NC for the renovated area. You might not have to exclude the addition as you described, since you'll probably be documenting the whole building performance for energy, lighting, and ventilation. If the work is less extensive, you might pursue CI for the new renovation work only. You might also consider pursuing LEED EB-OM for the whole building, and the renovation work would count toward the few credits that deal with facility alterations.

Hopefully the MPR supplemental guidance document and the LEEDOnline wizard will give you enough information to answer this; feel free to follow up here if it doesn't.