How many would you like to request it for?

Solution 1:

There is a rule of thumb to never end a sentence with a preposition. This "rule" is often broken; there are many clear and grammatical constructions that end a sentence in a preposition. Both of the following are grammatical and natural sounding (at least to my ears).

How many people would you like to request it for?

For how many people would you like to request it?

However, do note that I added the word people to both sentences. Although many can be used as a noun, the phrase how many always acts an adjective. In some cases, especially in dialogue, the noun can be implied by context:

I want some fish.

How many [fish]?

This pattern can also extends to prepositional phrases:

I would like to request it for some people.

For how many [people]?

But outside of this context, you should include the noun in the question.