I think in Lewis’ model, those sometimes interacting/sometimes not interacting Universes would be considered part of ONE Universe, operating under multiverse rules.
The flexibility afforded by this view is amazing to me. All the pressure goes away.
I’d still put them as part of one Universe operating under those rules.
That one Universe would contain a multiverse of non-interacting Universes, like two cells with thick walls that only briefly interacting under certain conditions within a larger cell.
So with this view, there’s philosophical room for the Bulk but also for Hawking’s no-boundary universe.
The Bulk is theoretically the dimension higher than our universe from which the Big Bang originated upon the interaction of two boundaries, or “branes”. Also called M-brane theory.