Should I start a new game plus?

[Guernsey]

I finished the game a while ago but I want to start a new game but I was wondering if I should because I hadn't fight Julius yet. Should I start a new game with all the spirits I have or continue my old one?

 

[Oracle Spockanort]

Why not do both? That's what I did. I have one save of my first playthrough and another save with my New Game + CM

 

[Guernsey]

I'll think I will beat Julius first before I do anything else although I am in Proud Mode and I didn't use EXP Zero.