The Neo 212 is listed, on the GK site, as handling 800 Watts RMS (not peak). Even if you take the usual (and usually prudent) step of assuming that translates to about 400 real-world Watts of power handling, you should be able to go with a more powerful head -- 175 Watts (if that's the case) into your cab is not much.
I had a Dr. Bass 2x12, some years back -- mine was 4 Ohms, not 8, but I imagine not horribly different from your GK cab in terms of max volume and real-world power handling (the cab was listed at 1000 Watts RMS power handling -- thermal -- which probably translated to about 500 Watts mechanical -- I know it wouldn't take 1000 Watts -- and efficiency was around 100 dB/W/meter, give or take a dB).
Anyway, playing that cab with my 300 Watt Mesa Walkabout, the amp was running out of steam on louder gigs. Played with a 500 Watt Markbass F500, I had enough to play comfortably where the WA was starting to compress and overdrive. It was a significant difference -- not as much as adding a second cab, but more than the "barely audible difference" folks like to cite on TB. Differences in voicing, etc., accounted for some of that, too, but not all of it (similar results playing that cab with a number of different heads in the 500-700 Watt range).
"More cab" is usually a better and safer solution for more volume than "more amp," but, in your case, I think "more amp" is worth a try. Can you take your cab to some stores and at least try it with a more powerful head? Is there a more powerful head that you could borrow for a gig? A 700 RB II or 1001 RB II would get more out of your cab than your current head (though, as always, with more power you'll want to utilize more care -- listen for signs of strain from your cab).
If you upgrade your amp and end up deciding that you still need more/better cabinetry, you'll still have a better amp to power the new cab(s) with (though, again, if you can try/borrow before buying, I'd do that).
In the ubiquitous "recommend my favorite cab" category (if you end up going that route), a 4 Ohm MAS 112 (particularly the latest, most compact design, if you're looking at navigating stairs) will smoke a GK 212 and excels at being heard clearly -- onstage and out in the house -- in a busy mix.
Finally, as Stumbo likes to say, an HPF can make a material difference in how loud you can safely go with a cab (more with some amps/cabs than others) and can be handy for boomy stages.