They have a bunch of picks and they seriously lack weapons on the offense. Edleman is all they have to catch the ball now that Gronk is retired. I could see them giving up a third to jump up for a TE or WR. Depending on who's there it wouldn't be shocking for the Rams or Chiefs want to move up. It all depends on who falls to us.
But that's kind of my point though. I think if someone like Hockenson is available, I could see them moving up. For anyone else though, why gives up picks for no apparent reason? The "weapons" in this class are all similarly rated. Why give up a day 2 pick for a guy that could realistically be available at 32? If that player doesn't fall, you're likely getting a very similar player. It just goes against the Patriots MO - they are incredibly patient and generally let the board fall to them.
Of course, all it takes is one team to fall in love with a player, but I think this is a tough draft to really count on teams giving up day 2 picks to move up at the back of the round. You can make a realistic argument that some of the guys in early round 3 could easily be taken in late round 1 and vice versa.
Again, I could be very wrong, but I think at 22, we're hoping for what happened last year with the Titans (conveniently when we were at 22) if we want to move back. A couple of smaller trades backs resulting in early day 3 picks rather than a big one that nets us a day 2 pick.