Anonymous (and myself) were right. You can't modify a word in a prepositional phrase, because the prepositional phrase isn't needed in the sentence. It's just added to give extra information. You really don't need to know that Dr. Stephens is "of those professors". The main subject in the sentence is Dr. Stephens. Therefore, the basic sentence is basically "Dr. Stephens=one". Okay, what about him? He does whatever it takes. The fact that he is one among many professors is extra info, which is why they threw it in a prepositional phrase. Once you remember that, you just take the prepositional phrases out of sentences to find the real subject. English 101....

According to the rules of American standard English, # 1 is correct. # 2 is not. If you say Dr. Stephens is *one*, you can't use "do" in the sentence. It sounds funny because it's incorrect English. Pretend that the prepositional phrase "of those professors" isn't in the sentence, then see how it sounds.

Dr. Stephens is one who does whatever it takes...
You get the point, right? You must think of the subject as being singular; therefore, you have to use "does" instead of "do".