The adverbs of quantity, like multe, kelke and sufiĉe, can function like nouns, i.e. be used as synonyms for multo, kelko and sufiĉo. This is explained well in PMEG. Zamenhof already made this synonymity apparent in the Fundamento de Esperanto, where one can find the following sentence:
Sur la arbo sin trovis multe (aŭ multo) da birdoj.
So in this sentence, "multe da birdoj" means the same as "multo da birdoj".
Of course, there are situations where only multe can be used, as an adverb is required. Here are some examples:
- Ni multe dancis dum la IJK.
- Mi multe amas ŝin. (Here one can also use tre instead of multe.)
- Ŝi estas multe pli alta ol li.
But whenever you can use multo, you can also use multe, and actually multe is more common than multo in situations where either one is correct. Here are some examples:
- Li havas multe/multon da mono.
- Mi havas multe/multon por rakonti.
- Multe/Multo okazis dum la pasintaj semajnoj.
Somewhat special is the situation with pluvi, which usually does not take a subject, but may take one, if one wants to indicate that something other than rainwater fell in a rain-like way (see PMEG). To say that it rained a lot, one would normally say Pluvis multe. Here pluvis does not have any subject, and multe functions in an adverbial way, not like a noun. But since pluvis can also take a subject, the sentence Pluvis multo is also grammatically correct. However, as pluvi is normally only used with a subject when something other than rainwater falls in a rain-like way, Pluvis multo would probably be understood to mean 'A lot of things rained', rather than 'It rained a lot'.