I think he should. Maybe just slightly alter the hair/makeup to distinguish this character from the previous franchise. But J.K. Simmons is spot-on and plays the character perfectly. Why fix it if it ain't broken?
The Amazing Spider-Man (2012)
Should J.K. Simmons reprise his role of J. Jameson in TASM sequel?
0
Yes.
It's been brought up before that Judi Dench played her version of 'M' in two different "continuities" of the Bond films. The same could happen here.
NO.
This movie is a totally different universe. Nothing should remind us of Raimi.
I think it depends on the direction. JK was fantastic, but this film did a good job trying to divert from the campy stuff. Only if JK can play the role slightly more seriously will I say yes.