Look at these sentences:
Note that in French, there are two ways to say "something else": autre chose and quelque chose d'autre.
Now look at these questions:
Vous voulez boire quelque chose d'autre ?Do you want to drink something else?
Do you want to drink anything else?
Do you want to drink anything else?
Vous voulez boire autre chose ?Do you want to drink something else?
Do you want to drink anything else?
Do you want to drink anything else?
Ont-ils apporté autre chose ?
Ont-ils apporté quelque chose d'autre ?Have they brought something else?
Ont-ils apporté quelque chose d'autre ?Have they brought something else?
Note that you also use autre chose / quelque chose d'autre in questions, where they can also mean "anything else".
ATTENTION: in the case of questions, you won't use n'importe quoi, which literally means any thing (doesn't matter what).
See N'importe quoi = Nonsense, anything (indefinite pronouns)
See also the related lesson: Quelqu'un, Quelqu'un d'autre = Someone, Someone else (indefinite pronouns)
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Examples and resources
Ont-ils apporté autre chose ?
Ont-ils apporté quelque chose d'autre ?Have they brought something else?
Ont-ils apporté quelque chose d'autre ?Have they brought something else?
Vous voulez boire autre chose ?Do you want to drink something else?
Do you want to drink anything else?
Do you want to drink anything else?