How many babies can you have on The Sims freeplay?

It depends on a couple of things:

If you are adopting and your adult sim is single, you can adopt up to seven children at a time. If you are married or in a relationship of some sort with a second person, or if there are other people in the household, make sure there are only eight all together (after you adopt). If you are reproducing, you can have a child, twins, or triplets at a time, depending on how many people are in your household. If you want a higher chance of having twins or triplets, earn up to at least 15,000 reward points to buy a "fertility treatment" on the list. It doesn't always happen, but it is much more likely than without. You can only have eight people in one household.

Tip: If your sim is all the way up to the very end of their "age stage" (such as young adult or adult) you cannot reproduce until they age up.

I hope this helped!