In science we attempt to classify everything. And everything seems to be a subset of something else. Planet is a part of a solar system, solar system is a part of a galaxy, galaxy is part of the universe, universe is a part of our dimension, etc.
Obviously there are exceptions to this, rogue planets, but we still consider them contained.
I understand the idea of multidimensions is theoretical, but if they exist, do we have a name or even a theory what might contain them?
I feel like the term you’re searching for is ‘multiverse.’ To me, it’s a literary term, I don’t know if physicists would use it in relation to the Many Worlds theory.