Yes, you can basically go through whatever motivation for your character that you would like. You could just be a highly trained assassin looking to exterminate all of the new 'supers' or vigilante cop that just found out he has super strength. 

I just have the Paradigm Stone as a plot point that any character can pursue for any reason. A scientist could try to experiment on the radiation it gives off, someone else might want to use it as a magical portal to an Asgard-like world and another might just want it to take over the mob. Someone else could just want to destroy the gem and keep others from having it.

But, again, the stone isn't even a necessary point at all.