The numbers don't work to end up with #25, #35, and #45. To drop from #14 to #25 would take a high second round pick, at a minimum, and the only team that is picking late in the round with enough ammo to do it is New England. They could trade #27 and multiple second or third rounders to make the offer, but it's the exact opposite of what they normally do.
As such, you're talking about having to make multiple trades with multiple teams, and that's just too difficult to predict. Add in that it looks like Harrison Smith may get into the late first, and it becomes incredibly unlikely.
Now if NE wanted to package both first rounders to move up, I'd have to think about it, even though we'd likely have to give them something back. And a trade back to around #25 that included next year's first would likewise have to be considered. But aside from that, I just don't see it.