You might be able to, but most rebuildables don't have the plastic center thing. Pretty much all the ones I have seen have had a couple posts with a wick and coil that gets screwed into the posts. I know lots of people mess around and figure out how to do amazing things like modding stuff to make it work better or rebuildable or whatnot, but there is a difference between this and having a product that was designed with the expressed purpose of being rebuildable.Even stardusts aren't manufactured to be rebuildable. The new ones have replaceable heads, but are not designed to be rebuildable per se.
Looking at the picture I see too many wicks so I would think It is possible. Looks like a stardust set-up. View attachment 127438