It all came down to Dean, really. Had it only been between Sam, Gabriel and Castiel, they would have gotten to this point months ago. Being angels, Castiel and Gabriel just naturally tended towards bonding in groups, which Dean jokingly had referred to as flocks a few times, and Sam was just plain tired of being alone, even when he was with other people. He hungered for closeness and touch, so it took him a shockingly short time to decide to put his last few doubts behind him, and dive into the irresistible offer of freely shared love and affection.
But Dean was another matter entirely. As much as he hissed and grumbled about taboos and “just plain wrong”, they all knew that his real issues lay deeper. After everything they'd all been through, Dean still didn't think he deserved anything. At all. Least of all love. So it was a monumental task to get Dean on board with the idea. Oddly, he didn't object all that much to being with any of them one on one. Even Sam, which was baffling considering Dean's main arguments for being against sharing. But none of them felt that calling him out on his contradictory statements would help them reach their goal, so instead they all just worked together to slowly guide Dean into their fold.
Gabriel in particular was impatient, because while Sam had loved being with both angels at the same time, he only did it once before deciding that he wouldn't do it again until Dean was there with them. Castiel agreed, which left Gabriel bitching and moaning about hardly even getting a taste of a decent love-pile before it was taken away again. Given that he'd been apart from the host for such a long time, Castiel could hardly blame him. He understood all too well the yearning Gabriel felt. But both Sam and Castiel each had their own deeply rooted connections to Dean, which just could not be overlooked. So Gabriel delved head first into the task of getting Dean with the program. And strangely, it was Gabriel who ended up giving him the final push.
Sam and Castiel exchanged looks of alarm when Gabriel finally snapped, and decided that Dean had been playing hard to get for quite long enough. In hindsight it was really hilariously simple. It took one shouting match between Dean and Gabriel. It consisted mostly of Gabriel screaming at Dean for being a complete selfish asshole, somehow managing to hurt three people at once, and ended with Dean going to a bar for several hours, and coming back to the motel surprisingly sober. He didn't hesitate, but simply stomped right over to Gabriel and yanked him into bed. Then he snarled at Sam and Castiel to get a fucking move on and join them, because “I ain't gettin' any younger!”
So to get him there, all they really had to do was convince him he was doing it for them. But more often than not, it ended up being all about Dean anyway, because they all just could not help loving him so fiercely. Even though he never believed a word of it. So the words were put aside, and instead they all spoke to Dean in the only language he really understood. They wrote their affection on his skin with fingers and tongues, pushed the taste of their desire into his mouth, and painted their love on him everywhere with bruises, bites and scratches, smearing their very essence on him, drowning him in sensations.
And once he was so thoroughly smothered in adoration that he stopped thinking altogether, then he was finally open to all they had to give to each other, comfort, love and trust flowing between them all equally. They could then at last take the first cautious steps to becoming whole again, after having been broken for so long. At least between them, they might have enough pieces to make one single complete puzzle. And that was enough.