We had Booker first for a year and a bit before Moosie came along. She seemed somewhat grumpy about his arrival at first (I remember one time she made a very loud grumpy bark when he ran through her bed while she was lying in it), but before long whenever we would go out we would find the two of them together on the bed and they have gotten along very well ever since. Moosie is very definitely not an alpha, and therefore there was no tension in that regard when Moosie arrived. Booker doesn't really play so Moosie never had that sort of a relationship with her either, but when Popcorn came along he found a playmate and they have been having a wonderful time ever since. I really don't remember either Booker or Moose getting perturbed when Popcorn arrived, but frankly she was just so traumatized for the first couple of months that she certainly didn't do anything that would have provoked either of the others. Booker and Popcorn have, I think, also developed quite a close bond - when we left them at a doggy hotel earlier this year they apparently hung out together and even slept together (which they don't do at home).
Buzz was accepted right away by Moosie (they drove home together from Edmonton to Vancouver) and absolutely adored Booker from the first time he met her (not-so-platonically at first, then less so since he got snipped!). And Booker seems to like him a lot too (especially now that he isn't QUITE as interested in her) and even will play with him a bit - which is VERY out of character for her. Popcorn, however, definitely had her nose out of joint for the first couple of weeks Buzz was here... there were growls, the odd snap, and a general feeling of displeasure exuding from Popcorn towards Buzz - but nothing too serious. I think Popcorn does have some delusions of being an alpha... when she isn't too terrified to act on them! After the initial tension, however, they have now definitely bonded - I think the turning point was when Popcorn realized that she could torment Moosie much more effectively as a team with Buzz than she could ever hope to do alone!
So I definitely think you need to give it some time and monitor the situation. The changes and acceptance tend to happen incrementally, as well, and so I suspect in a couple of weeks you will look back and realize how they have bonded without necessarily knowing that at the time.
Good luck and do keep us all posted!