someone else means another person, not someone more. i mean. if today i talk to you, and tomorrow i´ll talk to your friend, it´s not necessarily to talk to you before on that same day. so i say that it´s more correct to say "hablé con otra persona"
I also put "hable con otra persona". I agree that "alguien mas" means more like "I spoke to yet another person" rather than "I spoke to a different person", as I understood from the question. (Did you speak to the doctor? No, I talked to someone else.)