Semantics: Some answers are saying "no" by definition since "universe" means everything, including multiple different parts of a larger existence. However, that's not how the term is currently used and not how the question means it. "Universe" is a domain with spacetime as we see it, and a different such domain would be a different universe, as in the video referenced.
The answer, and whether the questions is even meaningful at all, depends on the model of cosmology you are using.
The question may be meaningless if different universes are totally separate and are not part of a larger structure that itself has space-like properties where things can move around, grow, and take up room.
One example of this is Cosmological Natural Selection. Each daughter universe is in a different spacetime than the parent's, disconnected from it. They are just different, not locations in a larger space that has coordinates.
Different Big Bang universes are not separated by ordinary space; the BB takes up all the space. However, the Eternal Inflation model would have it that there is a different state of vacuum (space-time) that is inflating at a much faster rate, and when it decays at some point to our vacuum then that point grows outward at a slower rate. Now the "outside" containing these bubble universes has a different interpretation of what is space and time dimensions than the bubble's spacetime inside a bubble. But they are connected in a meaningful way.
These bubbles are growing at a much slower rate than the space between them, so they could never collide.
A Braneworld theory is that our 4D spacetime is structure that exists in higher dimensions, and other such "branes" also exist and they are floating around and might possibly come into contact.
The Cyclic Ekpyrotic Universe model relies on that, where two parallel branes (one of them being our universe) collide and bounce off each other, explaining the Big Bang (the collision) and Dark Energy (attraction between the two branes).
Other models would have other answers, and different meanings for what such a collision actually represents.