Did all this arise because multiple smaller towns with their own survey grids got absorbed into the city at some point, or did the different alignments happen within an already-extant Minneapolis?
The cities merged because of competition with St. Paul, which had better rail access and was further down the river (didn't have to deal with the waterfall in Mpls).
So the original grids of both cities were created independently, however, once the cities merged they renamed almost all of the streets in both cities to be what is the modern day naming. This was mainly because there were many duplicate names on either side of the river. If they hadn't done this the street naming would be utterly confusing.
So the answer to your question is really "it's complicated".
https://en.wikipedia.org/wiki/Richfield,_Minnesota#/media/Fi...
Minneapolis extended down to 62nd street in 3 successive annexations.
Though, this had a pretty minor effect on the streets as they were already continuous.
[1] https://news.yahoo.com/news/milwaukees-bridge-war-story-behi...