On my table this past weekend we had a box that contained two thighs, two leg quarters and four wings. In such a situation each judge takes a single piece and the last couple people get whatever is left. I don't think it's good practice to send in a box this way because:
A) Your scores will be hard to interpret because each judge is sampling something different.
B) The last judges see the full box but the type of piece they wanted to try is not in the box when it gets to them.