In PIV multe has several meanings, including
II- Uzata subst-e., kun la signifo «amaso, granda kvanto, granda nombro»
Similarly, multo means
Amaso, granda kvanto aŭ nombro.
Both definitions come with a lot of examples but I can not see any difference between them. Is there any difference between multo and multe(II)?
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:
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:
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'.
It just depends on what allows for you to best articulate yourself. Multo is a noun, multe is an adverb.
Here's an instance where multo must be used because it can stand alone as a subject:
Multo estas riskata. [A lot is as stake.]
and for multe, in this case because it is describing a verb:
En Okinawa multe pluvas. [It rains a lot in Okinawa.]
You may see both multe and multo in something like "multe/multo da arboj", but multe is far more common. So I suppose use your own judgement, but personally I'll only use multo if it's strictly defined as a subject or object.
That is simple. You can use multo as a description of a big number of something countable. For example multo da tabloj. Like you say - ten, hundred, thousand - multo. And, sure, multo is a noun
Multe can be used as a description of something uncountable. Pluvas multe - "It rains a lot". Multe - adverb
