Could the Eagles trade back?

The Eagles currently hold only 6 picks in the draft. With many needs on the defense and a low pick that could have Philadelphia going best player available, is there a real possibility that Howie Roseman and the Eagles pull the trigger on a trade with a QB needy team possibly trying to swoop up and grab a fallen Teddy Bridgewater or Derek Carr? This could be the perfect scenario to get more picks in the draft, and to have more second round picks that can add players like a Jordan Matthews, Davante Adams or defensive players like safeties Jimmie Ward and Deon Buccannon. At 22 I have been debating between a wide receiver and a outside linebacker, but honestly Kony Ealy and Dee Ford are more 4-3 defensive ends that might not even be there. Plus the receiver the Eagles like in Brandin Cooks will most likely be gone as the New York Jets are reportedly really interested in the speedy receiver. This is the year that many teams are trying to claw back into the first round and get in on this deep pool of players (At certain positions as linebacker is thin). Why not grab more picks and let the Jacksonville Jaguars get Teddy Bridgewater? If I'm the Eagles, I would field every call for the pick and pull the trigger on the right trade. Cleveland seems excited about Derek Carr so they would be happy staying at 26, but at 20 the Cardinals may take Carr which would push the Browns to trade up to get Bridgewater (Or vise versa) to get one of their quaterbacks. I don't see the Cardinals taking a QB but if they do, many teams will be calling up the Packers and Eagles to get Carr or Bridgewater or whoever has fallen as they will be the last of the "Big Four". There is my rant for the day. This years draft is exciting no? So much better talking about all these trades and quaterbacks and receivers instead of those pesky offensive tackles. Go Birds!