[skissane]

Well, it is definitely possible by constitutional amendment, which normally means a two-thirds majority of Congress and 75% of the state legislatures. (Or the convention process...)

But, I don't think we can definitely say that a constitutional amendment is necessary. Suppose that a state requested to secede, and the request for secession was approved by both popular vote and by the state legislature; and that Congress then passed ordinary legislation approving the secession. Would the Supreme Court rule that legislation unconstitutional? I don't think anyone can really predict how the Supreme Court would act, but I don't think it is certain that they would rule it unconstitutional. But if it is possible that they might not rule it unconstitutional, it is possible that secession with Congressional consent is constitutional. Certainly it would be easy for the Supreme Court to distinguish this scenario from the Civil War scenario of attempted secession against the will of Congress, if a majority on the Supreme Court felt so inclined. If the majority of Congress, and the President, was in favour of permitting the attempt at secession, the Supreme Court might not be inclined to overrule them.

What counts is not what the document literally says, what counts is how it is interpreted in practice. And when dealing with hypotheticals, no one can really know how it will be interpreted in practice unless and until that hypothetical becomes an actuality.