Let me preface by saying that if there's on guy that the Rams like better than the others then they should stay put a draft him.
But if the Rams have 11 guys that they would be just as happy getting any one of them then yes, the Rams can (and should!) trade down.
Trading from 36 to 46 would guarantee that at least on of those 11 would still be on the board.
According to this draft chart [
www.drafttek.com] the Rams pick at 36 is worth 540 points. New England is at 46 and that pick is worth 440 points. NE could package #46 along with the 5th pick in round 4 (80 points) and the 7th pick in round 6 (6.2 points) to make the trade.
AlbaNY_Ram