Having another child could be considered a “change in circumstances” that would at least be grounds to get back in front of a judge to re-determine the support obligation. There is no guarantee, of course, that support would be reduced -it could even be increased.
This is a case where dads have seemed to have a real disadvantage in Lousiana. Judges almost always point out dads knew they had a child support obligation before they had another child. Lousiana code allows it to be considered as change of circumstance, but doesn’t require it.
I’ll add to that, briefly. If a dad does a child support agreement with the new baby-momma and any subsequent baby mommas and takes it to court and gets the judge to sign off (they’ll be happy to) it protects some of their income, because the judge figuring out child one’s suport has to take the other obligations into consideration if there are subsequent orders. Without an order, they don’t have to consider it an obligation. So if I were the dad, I’d sign on the dotted line; if I were baby-momma #1, I’d pray he didn’t.