You can get breeding pairs, although it's not easy. I've succeeded with humans and goblins, but don't think I've managed to get an elven couple. Animal people are very rare in my fortresses, so getting those to breed is almost impossible for me (one of the things I'll try [again] in the next fortress in the next DF version).
To get lots of races you need them to be abundant in your world, i.e. there are a lot of them in non hostile civs so some of them go about visiting other fortresses. Thus, you need to rein in genocidal forces such as goblins, humans, titan, and megabests.
A small dwarven population is easily achievable by setting the pop cap low to stop migrants from arriving.
In order to get couples, you need to have a large flow of visitors, i.e. a high visitor cap. I screen all petitioners using info exported from Legends Mode to Legends Viewer once per year to look up each petitioner (not mercs: I kick them out immediately, since they won't petition a second time) to check that the petitioner is married to an opposite gendered person who is still alive and moves around between fortresses as a scholar or performer of some kind (and thus has a chance to visit you to petition). In one case I did actually accept a petition from a merc spouse of a naturalized citizen and managed to get them to produce at least one kid.
A problem is that the tavern tends to get filled up with over stayers who just won't leave. Those block visitor slots from being filled with new visitors. There is no good non violent solution to over stayer problem (I don't consider kill them all/pour magma on them/atom smash them/use them as target practice... proposals out there to be either good or non violent).