Three states in their ratification documents said they could resume their own governance and four other states in their ratification proposed words similar to what became the Tenth Amendment, which is in many minds a legal basis for secession. I am reminded of Senator Jefferson Davis' word to the Senate on January 10, 1861:
...the tenth amendment of the Constitution declared that all which had not been delegated was reserved to the States or to the people. Now, I ask where among the delegated grants to the Federal Government do you find any power to coerce a state; where among the provisions of the Constitution do you find any prohibition on the part of a State to withdraw; and if you find neither one nor the other, must not this power be in that great depository, the reserved rights of the States? How was it ever taken out of that source of all power to the Federal Government? It was not delegated to the Federal Government; it was not prohibited to the States; it necessarily remains, then, among the reserved powers of the States.
Amend the Constitution? Two or three times in 1860-61 various Republicans in Congress proposed amendments saying that a state couldn't secede without the approval of other states, the president, etc. Why would they propose that if, as you appear to think, secession was already somehow prohibited by the Constitution?
Nowhere in the Constitution is secession prohibited. If you feel otherwise, please show me where it is prohibited.
You might also tell me how the Constitution would have been ratified if it had said states could not withdraw. Statements in the New York, Virginia, Rhode Island ratifications and the closeness of the ratification vote in those and some other states say a no-withdrawal Constitution wouldn't have been ratified. The government proposed by the Constitution was new and untried. States that had a few years earlier had to fight their way free of an oppressive government would be loath to put themselves in a position where they had to fight their way out again.
New York EXPLICITLY rejected the “conditional ratification” in its convention that was the occasion of Madison’s letter to Hamilton on the subject. So stop using that lie. The statements of other states do not say what you claim either.
In any case states could say anything they wished but the only thing that had any legal standing was the answer to the question of “do we ratify or not?” And the answer could not be “Yes, but...”.
The only minds the 10th amendment provides a legal basis for secession for are weak ones. No authority believes that.
States NEVER had “their own governance” to resume. They went from being colonies to being part of the USA. Most did not even have constitutions until Independence was declared. All realized that without Union they would have little chance of survival.
A constitution is the basis of the Union and like the foundation of a house cannot have part of it removed without endangering the whole structure. It weaves the states into a nation AND WAS INTENDED TO. It is a fundamental law. There are strictures within it dealing with the powers of the federal government to put down rebellion and insurrection even in states taken over by rebels against the constituted authority.
There was no need for a constitutional amendment to anyone understanding (or caring) what a constitution is.