Twins and Triplets are part of the Sims 3 mechanic but having them can depend on traits, family-oriented specifically, as well as if one or both of the partners have the fertility reward that you can buy with lifetime happiness points, 10,000 of them, if I remember correctly.
Listening to kid's music on the radio and watching kid's TV, can also increase the chances of having multiples.
But the sims also have to have space in their home, unless you play with mods.
I play with NRaas Master Controller(MC) as well as NRaas Story Progression (SP), and I've had former active sims who've moved out of the main house have, with both partners having the fertility reward, triplets, all fairies in my case, as the mother was a fairy!
But with MC you can also Instant Baby anyone in town and it will then ask how many babies you want to give them!
I've never done more than 2, so I'm not sure if there is a limit with this or not.
But I do know it's possible to 'over stuff' any household if you set it to do so in SP.
Which is how my family-oriented sim had a third child, despite owning 6 or 7 pets!
I believe the Instant Baby pathway is MC>Basic>Instant Baby>
If you've clicked on a specific sim and followed the above path, it will then let you choose Sim B, the donor.
Which is how I typically use Instant Baby.
For the donor, I choose household, to have their spouse/partner be the father of their baby, but you can pretty much choose anyone, as far as I know.
I'm sure others that love and play large families may have other tips and tricks for you too.