Not affiliated with the US Social Security Administration
You'll need to work more with SSA as I can not find a definitive answer. However, based on my reading, the benefit for the remaining child will not increase.
The family maximum seems to limit benefits for a family to 150-180 percent of the parent's full benefit amount. With only one child, a child may receive up to 75 percent of the deceased parent's basic Social Security benefit. Two children combine to receive 150 percent of the deceased parent's basic Social Security benefit. However a third and fourth child would start to see the effect of the family maximum.
In other words, if you had three or four children, as children graduate, the remaining children would see an increase in their respective benefit until you had two children receiving benefits. As the second-to-last child graduates, the remaining child would not see a benefit increase; they'd already be at 75 percent of the deceased parent's basic Social Security benefit.
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