My overlaps are generally either:
A) A map constraint (such as to get a port)
B) Captured cities (and I'll often use poorly placed ones as a farm making settlers/engineers, drawing down the population until it no longer exists and thus no longer causes overlap)
C) Cities gained early from a hut/goody box (depending on the size I may draw them down too, but sometimes they are needed early on and are prohibitively large or developed by the time they can become candidates for being settler/engineer farms)
In my current game I have 253 of the 255 cities and the total overlap is probably about 30 squares/tiles.
If you are willing to take the time to do so, food caravans can overcome the size restrictions from overlapping. Do them enough and it can even overcome the point restriction from having fewer working citizens that can be counted at two points each (if happy).