Take another look at the sentence:
Not only did Dennis apply an extra layer of deodorant to his armpits, but he also polished each tooth with special care. He did not want to offend Malinda with any unpleasant odors.
When you use not only ... but also, you must maintain parallel structure. Since Dennis did apply ..., a main clause, follows not only, a main clause must also follow but also. He polished ... qualifies, so the sentence is parallel.