Just for fun I looked at the trade value charts to try to get a sense of what things would cost the Patriots to move up in rounds 2 and 3. I used pro football reference, which seemed to be about middle. Obviously, this is an inexact science, but fun to think about.
Points to Move Up
46 to 32: 150 points
46 to 38: 80 points
46 to 42: 40 points
76 to 58: 110 points
76 to 62: 74 points
76 to 66: 50 points
76 to 70: 30 points.
Value of Patriots' Picks
107: 80 points
117: 60 points
120: 54 points
135: 39 points
184: 18 points
192: 15 points
Thereafter: Just assume around 10, give or take
So, a move to the bottom of the second round, assuming they give their top 3d round pick, would take at least the top two fourth round picks, and maybe a sixth. A move up near the top of the third round would take pick 107. Etc.