Function of Else

In the sentence, "Do you study anything else besides English?", what is the function of else?

The OED gives else, adv., adj., n., and conj. (different/other/additional)

Part 1

The adjective

One argument is that “else” is an adjective: (different/other/another/additional)

The meaning of "Do you study anything else?", is "Do you study anything that is different/additional?", and “anything” is a noun. Therefore, “else” is a post-positional adjective.

"Do you study anything besides English?" shows “anything” to be a noun (in fact, an NP = determiner + noun.)

A: "Do you study maths?"

B: “No.”

A: "Do you study anything?"

B: “Yes, English.”

A: "Do you study anything else?" = "Do you study any different/other/another/additional subject?"

B: “Yes, I study French.”

In which we can see that “You” is the subject, “do study” the verb and “anything else” is the NP object.

With the addition of “besides English”, semantically, the theme is not “study”, it is “English” and “anything (noun)” is looking for alternatives/additions (within the category of nouns) to the noun English, and not an alternative or addition to, or modification of, the verb “study”.

Part 2

The adverb

The argument is that “else” is an adverb, and this is supported by OED, which classifies this use as an adverb, in the meaning of “otherwise / differently / additionally”. Which gives the meaning of "Do you {otherwise study}/ {study in addition} anything?"

However, there is the adverb “elsewise” that, were it required, could be used.

1864 C. Dickens Our Mutual Friend (1865) I. i. xi. 97 Elsewise, the world got up at eight.

Part 2a

The flat adverb

If “else” is an adverb, then it is a flat adverb.

Whether The flat adverb exists is a matter for discussion but the Wikipedia article https://en.wikipedia.org/wiki/Flat_adverb states

In English grammar, a flat adverb, bare adverb, or simple adverb is an adverb that has the same form as the corresponding adjective, so it usually does not end in -ly, e.g. "drive slow", "drive fast", but sometimes does, e.g. "drive friendly".

Flat adverbs were once quite common but have been largely replaced by their -ly counterparts. In the 18th century, grammarians believed flat adverbs to be adjectives, and insisted that adverbs needed to end in –ly

[That last sentence would have been better as In the 18th century, grammarians believed flat adverbs to be adjectives, and insisted that if a person wished to appear educated then their adverbs needed to end in -ly.]

The alternative view is that these flat adverbs are, in many cases, resultative or depictive adjectives that are free modifiers of the clause in which they appear.

He shot her dead / He shot her fatally but *“He shot her deadly.” She shouted herself hoarse / * She shouted herself hoarsely.

And we can see a difference in “He arrived drunk” and “He arrived drunkenly”

The flat adverb may still be encountered colloquially “He was dead accurate with his shot.” Or “Hold fast!”