I recently read in John Maxwell's book Attitude 101 that Goliath had four sons [or brothers, in some versions]. Maxwell explained that the reason David grabbed five stones is that he needed one for Goliath and one for each of them. Maxwell said he got this insight from 2 Samuel. However, I see no such evidence. What do you think?

Maybe. That is a common opinion and it preaches well.

I do not know how it can be proven, though. 2 Samuel 21:22 gives a few biological facts about the giant's family. But how can we access David's inner mind or know his plan that day in the Valley of Elah? All we know is that he declared war on Goliath, who had insulted the living God.