The concept of a multiverse does not necessarily imply that multiple universes exist within a single overarching space or container. In many interpretations, including the widely discussed inflationary multiverse hypothesis, the idea is that multiple universes can exist independently and parallel to one another, each with its own space and time.
The expansion of our universe, as described by the theory of cosmic inflation, refers to the idea that space itself is expanding. It does not mean that our universe is expanding into a preexisting empty space. Instead, it suggests that the distances between galaxies and other cosmic structures are increasing over time.
In the context of a multiverse, each universe would have its own expansion and its own space-time fabric. Universes within the multiverse may undergo independent processes of expansion, contraction, or other transformations. So, the expansion of one universe does not necessarily affect the expansion of another universe within the multiverse.
It's important to note that the concept of a multiverse is still a topic of scientific exploration and debate, and different theories propose different mechanisms and structures for a multiverse. Therefore, our current understanding of the multiverse is speculative, and further research and evidence are needed to confirm or refine these ideas.