Kind of like a shower thought just occurred to me. We've all seen lots of animation about spiral galaxies, how they crash... in virtually all of them, I recall they move in a frisbee way, that is their velocity vector is on the same plane as their disc. That sounds wrong... right? What keeps them from tumbling in a random direction in space? Why can't they move like an American football? Or a tossed coin? You know, all the stars within can still go around merrily, but nothing is keeping the whole spiral from moving in a chaotic way.
Before you say that I'm completely wrong to even speculate that, think of our neighbor Andromeda. Fact: its angle to us is not completely edge-on, perhaps 25deg. Fact: many scientists @NASA & other great institutions made high-confident predictions that we're on a head-on crash course with it. Just those 2 facts mean Andromeda OR Milky Way can't be moving along its own plane (or both, lol).
EDIT: when I said galaxies I meant spirals in particular. Also, I think the question above can be rephrased as: in the case of us & Andromeda, what will we see during the next 4.5Gy? Will we see our sister galaxy tumbling while coming toward us, i.e. its angle changes, its appearance dramatically transforms, not just getting bigger in apparent size?