Quoting: rangersandislesfan
Say Seattle only has one trade left. They want to trade player A to Houston for player B, and they want to trade player C to Kansas City for player D. They could make a 3-way trade that sends player A and a 7th round pick to Houston for player B and a 7th round pick, when Seattle would then trade the 7th rounder from Houston, to Kansas City with player C, in exchange for player D and another 7th round pick. All it would do is swap picks plus do exactly what Seattle wanted to do with 2 trades, even though this is 2 completely different trades put in to one.
I'm not sure I understand your example. If I'm reading it correct, you are inferring that it's only the picks being swapped between all three teams, which if that's how you mean it, it has no bearing on this being a 3-way since we've long established that moving picks doesn't count toward trade limits.
I'm pretty sure something has to be exchanged between all teams in regards to contracts as mentioned in the post above mine.
So team A gets Joe, Jim and 1st from team B
Then Team A sends Jim to team C who now sends Jeff to team B
Something like that. Hope that helps since it's hard to envision without it being more realistic.
But basically ALL teams must be receiving something in the overall deal.