Getting more 2nd round picks is really just a matter of cash, on draft day they are often traded just for $$$, even the early 2nd round ones. Basically they have very little value at this point (odd, but proven the last few years when they are traded for cash)
Honestly, I would love to package a few to get a 1st round pick, but I would do it for a future pick and hope that it became something above #20. After about #20 these picks are not particularly valuable.