Is this sentence grammatically correct?
we sound better than you or me.
Shouldn’t we use “I” instead of “me”?
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There is a lot of debate around 'than I' and 'than me'. The confusion comes from the fact that 'than' can be a conjunction or a preposition and therefore both can be correct.
If using the conjunction form, as Kate mentioned in the comments, it is better to add the verb in as well: "It sounds better than I do". This will always sound (and be) correct as the verb makes it clear you are using 'than' as a conjuction. "It sounds better than I" is also correct but may sound incorrect to people who use the preposition form. (Hence the arguing)
If using it as a preposition then it should be "It sounds better than me".
For other cases were you need to pick between 'you' and 'I':
Both words are pronouns, but I is a subject pronoun while me is an object pronoun. Here the word is being used as an object so 'me' is correct. A trick that may help is to remove the other object from the sentence.
"It sounds better than me" - Correct "It sounds better than I" - Incorrect
This is a confusing sentence. "We" and "you or me" seem to be referring to the same people. So it is strange to say that one sounds better than the other.
If you mean that together they sound better than they do apart this should be explicit. Something like: "We sound better than either of us individually"