I remember it happening not that long ago but I'd have to go back and dig to find the actual team and how far they ended up trading down. I seem to remember someone trading down twice into possibly the 20's even. But I can't remember exactly which team it was. They ended up taking someone really disappointing too if I remember.
Don't recall a double trade out of the top 10, but here are some that happened:
2013 - Miami traded up to #3 with Oakland who dropped down to #12. They took Dion Jordan and Oakland got D.J. Hayden and Menelik Watson.
2008 - Jacksonville traded up to #8 with Baltimore who dropped down to #26. They took Derrick Harvey, the Ravens traded most of the picks, including a 1st, 2 2nds and a 4th. Took Tavares Gooden in the 2nd.
1999 - Ditka traded his entire draft for Ricky Williams to move up to #5 from #12.
Might have missed something else, but usually trading into that realm does not seem to work out well, sometimes for both teams.