How do you renounce citizenship anyway, even if you wanted to? You could give up your original passport to the other country's officials, but that wouldn't stop you applying for another any time later.
Officially the US doesn't allow dual citizenship, but my sister took US citizenship after her American husband died, partly because it made the tax situation simpler - she had already lived there a long time. But she always intended to keep her British passport and at the naturalisation ceremony the official even told them that they know a lot of people do this - they just turn a blind eye.