Is there an equivalent of "Me neither" as a standalone sentence in Japanese? I know you can say the whole sentence (e.g. "I also can't understand"), but what about "Me neither" on its own?
You can just use 「私も」, 「俺も」, 「僕も」 and such. They can mean both "Me, too" and "Me, neither" depending on the previous statement.
You can use も in your sentences.
私もです Me, too.
私もできません I can't do that thing either.
私も分かりません I also can't understand.