Thanks for the updated demo. I think I understand what you're trying to do.
You have a set of elements that you want to stagger, but on the first pass, element should not be a part of the stagger, correct? On iteration 1 element is going to do its own animation, but every repeat thereafter it should be a part of the stagger array?
If that's the case, there would be a number of ways to make this happen. For simplicity I just made a couple new demos with some divs so we can clearly see what's going on. In this first option I have made two arrays. One with all the boxes and one with all the boxes except .box1 using jQuery's .not() selector. You'll see the result is box1 animating its y position on the first tween and boxes 2-5 rotate. After that, all 5 boxes rotate.
Another option would be to create the target array and then splice out the first element. You'd then play your first iteration of the animation and onComplete call a function that recreates the array and staggers all the elements in a new stagger tween. It's the same result, but just a different approach.
Personally, I'd go with the 1st option as it's a bit simpler. The bottom line is you need an element to be part of an array for one stagger animation, but not part of it for another so I think that takes a creating a couple arrays or modifying one. Others may have additional ideas better than mine. Hopefully that helps.