Yes, our "North Star" does rotate around our galaxy. And, our galaxy rotates around the center of mass of our neighboring galaxies. The more our astronomy capabilities progress, the larger the groups of things in larger orbits are perceived. For all we know, what we call out "universe" may be just one part of something far bigger, in even larger orbits. Perhaps everything within 13.8 billion light years (or whatever its current proper distance is estimated to be), is just a blob of stuff in an orbit trillions of light years in diameter. Etc.
Until only about 100 years ago, we did not even perceive that we are in a galaxy and things like the Andromeda galaxy are not part of our own.
BBT proponents will probably chime-in to tell us that something like our "universe" orbiting anything is impossible because (they believe) that space is expanding too fast for anything that large to have a closed orbit. Maybe they are right. But, maybe not. Maybe there are other parts of space that are contracting while our >13.8 billion light year "little" part is expanding. If it really is expanding. Remember, the BBT is a theory, and previous theories astronomy have been giving way to larger and larger universes throughout our history.