This was exactly what happened with Spanish flu. Erupted in early Spring of 1918, spread widely until summer, and then a mutated form caused a bigger and deadlier second wave in the Fall. A third wave occurred the following Spring with an equally high mortality rate, but the death toll was lower, likely due to the decrease in troop movements after the war.

Luckily for us, a coronavirus is generally less likely to mutate into more a lethal form than is an influenza virus.