"I don't know any more than you do"

Usually, the intended meaning is "I know just as much as you [do]."

My level of knowledge is the same as yours.

It often is said with the meaning that neither of us has much knowledge.

It's usually said about specific knowledge.
eg
Q - Will the plane arrive on time?
A - I don't know any more than you do.

contraposition"I don't know any more than you do." What does this sentence mean?

It means literally what the words say. The final 'do' is the pro-verb for 'know'. It's used as a response to a question.

The practical meaning in most cases is "You are asking the wrong person, because I don't know the answer either