The devil is in the detail
I am rather surprised by your definition of "Universe". I was brought up to believe that Universe meant "all there is", not to mention all there was or ever shall be. Thus any system within "The Universe" might be termed "miniverse" or "semiverse" or possibly some other diminutive appellation. I find it very "off-putting" to see smaller or multiple versions of "all that exists" etcetera. Conversely, you might call "our Universe" by one of these diminutives, but then I suggest that that would be begging the question, in that some "clever" person might decide that the Universe was actually just part of something bigger.