I am not sure how nice the modern Sram stuff would play with a 2x setup. I know for a Shimano system you can use a WolfTooth TanPan and a long cage XT/XTR rear derailleur to accomplish what you're asking.
I ran a 36 tooth cassette with the same derailleur; no modifications and no issues. I then ran (am running) a 40 tooth cassette with the same derailleur but require a Lindarets Road Link to do so. I've done this on two different bikes. Below is the latest iteration. The derailleur is cut off in the pic, but you can see the Roadlink. This was a rather unique set-up, 46/30 up front and 11/40 in the back. The gearing was needed to ascend Mauna Kea on the the Big Island a couple weeks ago. This won't be a full time set-up as there is cross chaining in small/small. However, I have run the 11x40 in the rear with a compact crank full time with no issues.
s0ldats wrote:i found this thread: http://ridinggravel.forumchitchat.com/post/mixing-sram-rival-22-with-gx-8435141
looking into that fsa crank!
That thread is only semi helpful. Kind of like this one.
What you are wanting to do can be accomplished by using the SRAM GX 2 x 10 rear derailleur (or any 10 speed SRAM mountain bike rear derailleur, but you probably don't want the X5 because it doesn't have a clutch). It will for sure clear a 36, maybe a 40, and maybe (to a lesser degree) a 42 depending on your frame. https://www.sram.com/sram/mountain/products/gx-2x10-rear-derailleur (you want the long cage). I have one on my fat bike and it for sure clears a 40, but the derailleur hanger is purposely longer on that bike. It's *likely* that you could run an 11-36 in your current setup without any modifications or extra parts besides a new chain.
The cable pull is the same between 10 speed SRAM mountain and 11 speed SRAM road (and 10 speed SRAM road). Basically that means the 10 speed SRAM GX rear derailleur will act like an 11 speed rear derailleur when being shifted by an 11 speed road shifter.
Not sure about Rival 22, but my Vaya came stock with Apex brifters, FSA 48/32T cranks, a GX 10-speed long-cage rear mech, and a SRAM 11-36T cassette. I swapped out the chainrings for 46/30T and the cassette for a SunRace MX3 11-40T. Nothing further was needed -- same chain, no derailleur extension -- and shifts have been fine. I suspect I could even go up to 11-42T if I needed to.
Thank you for the advice everyone! i'm going to try an 11-36 cassette first with my 'stock' setup since I have one lying around. That should give me enough range with the 50/34 rings!