Possible, yes. Add an ebay and top tube, electronics, and appropriate recovery materials. Tube and electronics bay from LOC is $46.75 plus shipping. That's almost half another rocket. If I had to do it again, I would L1 on a 38mm motor DD bird on single deploy, learn DD on that same bird at L1 altitudes and the cheaper L1 motors, then build an L2 bird with a 54mm motor mount and buy a motor mount adapter, confidently stepping into L2 with a bird, electronics, and skill sets that were fully suited to L2.
LOC advertises the kit as F, G, and H capable. That probably has a lot to do with it being single deploy. Pain in the butt to go chasing a pop-n-drop that's 3K feet up in the air and going downwind FAST, so that's probably why I and J's aren't part of their recommendation more so than any other factor.
Sim in Open Rocket or RocSim so you know what you're getting into. Open Rocket is free, easy, and runs on just about any platform that will run Java, so there's really no excuse NOT to be using it, especially as you quest for other designs and motors.
What it really comes down to is, once you've settled the question of CG and CP with the sim: Did you build the booster strong enough for L2 motors to begin with?