When drinking Zamzam water with the intention of "Zamzam water is for that for which it is drunk," is it sufficient to have a single intention, or to have multiple intentions, or to drink the water multiple times with different intentions each time?

The Hadith "Zamzam water is for what it is drunk for" is authentic. It indicates that Zamzam water benefits the drinker for any purpose he intends, whether worldly or related to the Hereafter, because the word "what" (ما) denotes generality. Many scholars have drunk it for specific needs and achieved them. There is no difference between intending multiple matters with a single drink or drinking multiple times with a different intention each time.