The most famous serial killer of the year has gotten very lonely. Wishing to have a friend who would accept him, joins a support group with very different and grotesque addicted people. One of those people is an overworked Agent who is part of a case to catch the most famous serial killer of the year.

I think the main character needs a clear end-goal. As it is now, the only goal presented in the logline is "to find a friend", but as far as I understand it, he finds that early on in the movie (when he joins the group). He also needs a main action, something he must do to reach his goal. Maybe he needs to cover his tracks before before the Agent finds out he is the killer, in order to keep him/her as his friend?

Also, this logline could be boiled down to a shorter one. Including the main action and the goal, maybe something more like this:
"When a lonly serial killer joins a support group and take intrest in an other member, an overworked agent who is assigned to solve the murders he commited, he must cover his tracks before she finds out he is guilty in order to keep her as a friend."

Hope this helped :)

Has an unusual premise, though I'm not sure what the dramatic question is?