What is the meaning of Mögen?

to like (something or someone)

would like; to want (something)

would like; to want [with dass (+ clause) ‘for someone to do something’]

to want to; would like to; to wish to [with bare infinitive ‘do something’]

to want; would like (similar to möchte)

may

may; might; could

to be hesitant to (do something)

may; be .

to be able to, can

may, can, be allowed to.

used to express presumption, often used as the English should

to wish to, to would like to

often used with glöven or seggen, emphasizes their meaning

to be allowed to have/take, to may have (used as a polite way to request something)

To like.

Source: wiktionary.org