We all know that Jane's goal is to find and kill RJ, that is a foregone conclusion. I pose this question though, what is RJ's purpose? If it was simply to kill random people or mess with Jane then there would be no reason for him to be associated with so many people when even one loose end could result in his identity being revealed and him being captured. I have a few theories on his purpose, because keep in mind he was killing people before Jane even mentioned his name on T.V. and his wife and daughter were murdered by him.
1. He's like the Joker from Batman and just wants to see the world burn.
2. RJ is leading some sort of revolution. Its been hinted he was a member of visualize, and I believe he was Brett Stiles protege until the student surpassed the teacher and became dangerous to even Stiles himself. This leading to RJ needing a good number of followers to take down visualize and him having the techniques to do just that.
3. RJ ultimately wants power. He will do anything and everything to have control of as many different organizations as he can regardless of who he has to kill. Remember how he killed Bosco's team so Jane could be back on the case and the CBI just obliged and said OK. I didn't know that police organizations gave into criminal demands so easily.
4. In no way do I think Jane is involved in RJ's purpose or grand plan I just think that Jane got caught up in the middle of it with his comments and is one of the few people who intrigue RJ in terms of brilliance and so RJ toys with him. Don't kid yourself by saying Jane is smarter than RJ because time and time again he has been outsmarted and maneuvered. It's a game of cat and mouse RJ has enjoyed playing.
His purpose could be completely unrelated to any of what I just said and I could be completely wrong, however I feel as though it will be much easier to figure out who RJ is once his purpose or goals have been established.