nest together
1. To fit into the space or spaces of one another in a neat, compact manner. My luggage set all nests together when you aren't using it so that it's much easier to store.
2. To fit something into the space or spaces of one or more same or similar things in a neat, compact manner. In this usage, a noun or pronoun is used between "nest" and "together." Tom, please nest the pots and pans together in the cupboards—it turns into a jumbled mess in there otherwise.
nest together
to fit together or within one another compactly. These mixing bowls nest together. I want some of those Russian wooden dolls that nest together.