That's what you mean by a range of genres? Same game, same classes, different weapons & armors (Ok, and social structures)?
That's eminently do-able from 3e on, little more than re-skinning gear is required. Mail becomes mammoth hide, broadsword becomes macuahuitl, wizard's spell book becomes cave paintings...

OK, notched sticks & bones and bits of crystal for his traveling spellbook.
Steampunk's surprisingly easy if you're up for re-writing spells as technology (Myrlund famously did that back in the day, no?), easier the more amenable to re-skinning the system gets. You can go sci-fi be crossing over with gamma world with little issue.
But edition /barely/ matters in that. You had Expedition to the Barrier Peaks, Six-guns & Sorcery back in the day. All the WotC eds (I'm pretty certain 5e didn't change this) let you re-skin /gear/, which is all you need to shift technology so long as you can make a case for the weapons/armor arms-race keeping pace (which is an oversimplification when you get to modern firearms, but could be fine for steampunk & sci-fi).