Yes, it can and usually does. After the other growths mature, the original old growth can send out a new one. I haven;t had this experience with multiflorals yet but I assume the same holds true -- as long as there are active eyes.
I've had this more with multis than other groups. I've had bloomed growths on a few multi species start up to 5 new growths at once, but 2-3 is fairly common.