Learn Finnish: En pidä tästä automaatista, onko teillä mitään muuta? - I don't like this automatic, do you have anything else?

Muu is used for "other" or "else" when referring to something of a different kind or category. If you used toista (from toinen), it would mean "another one" of the exact same kind — like asking for a second, identical machine, rather than a different option altogether.

Why are the words mitään muuta in the partitive case?

In Finnish, abstract or unknown amounts are expressed in the partitive case. Because you are asking about "anything" without a specific object in mind, it takes the partitive. The word muu simply matches the partitive case of the pronoun mitään.

Why does the sentence use tästä automaatista instead of just the base form?

This is a classic rule to remember: the verb pitää (when it means "to like") always requires the thing you like to be in the elative case, which ends in -sta or -stä. Both the demonstrative pronoun tämä (this) and the noun automaatti must take this ending.

Could I say onko teillä jotain muuta instead of mitään muuta?

Yes, but there is a slight difference in tone. Mitään is used for open-ended questions meaning "anything at all," which fits well after expressing dislike. Jotain means "something," so asking onko teillä jotain muuta? sounds slightly more like you expect them to have a specific alternative to offer.