I’m noting this down so I can revisit it when I have time to research this.

In Cypriot Greek, the verb μάχουμαι has at least the following meanings:

• to put effort into doing something

Example: /'maxume na a'kuso 'tambu la'li/ (I’m trying to hear what he/she is saying - adapted from here).

• to annoy, to annoyingly demand

Example: /'panda 'maxume su na 'ertis/ (I’m always asking you to come - from here. “Stop bothering me” is /'men mu 'maʃese/.

What about the following use though?

A: /'eteʎoses tin erɣasian su/? (Have you finished your essay yet?)

B: /'maxume/ (I’m working on it)

That is clearly not the second meaning, the second meaning requires a recipient (usually a living thing, not exclusively though). It’s very similar to the first meaning, but it also feels a bit different: Meaning 1 takes a subjunctive verb as complement, and this use doesn’t. Also, Meaning 1 emphasises the effort required to complete that task. This use emphasises the ongoing aspect.

I could find one spontaneous metalinguistic comment online:

A: If you had a Cypriot/Greek version of this, it would be awesome!

B: /'maxume/, the so-called work in progress

This person glosses /'maxume/ as “work in progress”.