There is a cheat but it does not work, so no you cannot have triplets.
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There are no cheats for triplets or quads. But it can happen naturally.
Not naturally, if you want to have triplets then you have to have a download a mod for multiple births.
You need the Insimenator.
It Is Luck To Get Triplets I Usually Get 1 But U Can Get Pregnant On Any Sims 2 Game [On PC] And If U Want Triplets You Need A Cheat "CTRL+SHIFT+C" Brings The Cheat Box Up And This Is The Cheat "ForceTwins" Without The " Then When She Has Her Baby/Babies It Will Say There Is 2 Babies On The Way And She Will Have Twins TA-Da!!
You can only have triplets.