Good idea. You can actually handle this as a spin-off without the need of doing what the series did. The parasytes are not only in Japan, right? So just take the premise and involve someone with completely different circumstances than the original protagonist in that mess. Thinking of Shiki, just imagine a woman or man some day realizing that her or his small town is getting weird lately. Some people are off and while nothing of notice seem to happen, the protagonist starts investigating. What at first looks like paranoia and mental illness, gets really bad, when the situation gets so severe that he isn't the only one that starts to see it and people start dying. Further this with the question if humans are so much better than parasytes, parasytes developing emotions, doing experiments, etc.
I think the added layer of paraystes actually having intelligence without being way above humans in that regard can be very interesting and the relationship of the protagonists to these beings could be even more interesting, if he isn't bound to one himself.