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Sure you can. You can have 4 projects with 1 repository and then do lots and lots of cross-project merging. It could get quite difficult to manage/track what has and has not merged.
But I'm sure you've already thought of that so you must be looking for something more...
It would be ugly but you could have one project with 4 dev states that map to a single dev view, 4 test states with on tst view... That is you could have the states WebDev, WebTst, WebPrd, FinDev, FinTst, FinPrd, ...
and all the DEVs share the same Dev view and all the Tst... However, I wouldn't recommend this. It really isn't any different than having 1 with 1. Any Dev state can update any item. So you'll only have different approval and promote processes and that can be done using 1 with 1?
Anyway, what are the requirements for the problem that you're trying to solve? why do the 4 projects need to share 1 repository? why can't it be 1 sharing 1? or 4 with 4? or 60 with 20, or 60 with 60, or 20 with 20.... Why won't those work?