There is a family max. You won't get over that amount, regardless of number of kids.
There's an amount you get per kid, I think it's up to age 18. It's extended until they graduate high school up to 19 I believe (so if your child turns 18 in December of their Senior year, they'll keep getting payments until they graduate high school in May/June). On top of the amount you get per kid, you also get an amount for yourself IF one of your kids is under 16. Once they hit 16, YOU don't get a payment anymore, though your kid will until they turn 18 (or later, see above).