Is there a saying to the effect that when a person has a sucess, another soon follows?
2 Answers
on a roll (thefreedictionary)
in the midst of a series of successes
There's also the equivalent (but somewhat less "slangy") winning streak.
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1Even just I'm on a roll is now far more common than Nothing succeeds like success. Allowing for Past Tense and different subjects, the "roll" idiom will be vastly more common than the "quirky saying". But I'd also say that usually, the quirky saying refers to being predictably "socially" successful (the rich get richer, because that really is how "the system" works), whereas being "on a roll" is usually just a matter of blind chance. Commented May 10, 2021 at 15:52
It never rains but it pours means pretty much exactly what you want. I've heard it most often refer to bad things, but The Free Dictionary says it can be used to refer to good things as well.
The construction is a bit archaic; read it as "The only time it rains is when it's a downpour."
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1I suggest this idiom is almost never used of good things. I see no reference to that possibility in Merriam-Webster or Collins, for example. Commented May 10, 2021 at 14:48