I always thought the universe is expanding to a larger universe. I never thought that it could be expanding to something else.
Two assumptions:
a) the universe is infinite. In this case it doesn't expand into anything, the things inside of it just stretch apart.
b) the universe is finite. In this case it expands into something, but because we're trapped inside spacetime, we can't answer this scientifically.
The wording "expanding" adds more confusion than it helps. See [1] for the discussion about this topic.
[1]: http://curious.astro.cornell.edu/ask-a-question/104-the-univ...
Any metaphor you hear about a balloon or fabric or things like that is an overly simplified version of complicated mathematical models of the universe.
Here's more to read about it:
https://www.quora.com/Astrophysics-If-the-universe-is-expand...
https://medium.com/starts-with-a-bang/ask-ethan-if-the-unive...
Wow... and this person went to Harvard??