There were various proposals before the 25th Amendment to solve the problem of presidential succession in the event of a vacancy in the vice-presidency (it was noted that after 1954 the next in line after Eisenhower and Nixon was Speaker Rayburn, and some thought it wrong that a double vacancy in the presidency and vice-presidency could lead to a president of a different party without a new election). Some of the proposed solutions would require a constitutional amendment, but one would not: to create a new office (sometimes called the Deputy President or First Secretary) who would assist the president while being next to the vice-president in the line of succession.
I had a soc.history.what-if post which now seems lost but part of which I quoted here (I think this is a direct quote from a book):
"The Rockefeller and McCarthy proposals are constitutionally sound. This is because Congress has the power to create an office of First Secretary or Deputy President under the Necessary and Proper Clause of the Constitution, and the power to invest the occupant with a place in the line of succession under the succession provision. But Congress could not, by statute, give such an office the power to preside over the Senate (this is the exclusive duty of the Vice-President or, in his absence, the
President pro tempore). And the method of filling the office is limited: appointment by the President, by and with the advice and consent of the Senate, as in the case of any other executive appointment."
https://www.alternatehistory.com/fo...g-a-vp-vacancy-pre-1967.403862/#post-13651300
This, it seems to me, has better chances of passing that the creation of an actual "second vice-president" which would require a constitutional amendment. IIRC, Vice President Nixon was not happy about any of these proposals, feeling that the vice-presidency was too weak as it was, and creating a second vice-president, whatever the official title, would only weaken it more.
Apparently Hoover's idea was to create "an office of 'Administrative Vice President of the US.' He was to be appointed by the president, confirmed by the Senate. He was not to be an elected official. [I do not know whether he was to be in the line of succession, but probably not because from the description his tasks would be purely technical and routine--e.g., 'approving concert tours for armed services bands!'--DT]. President Eisenhower does not favor use of the title 'vice president.' That office has a constitutional function which the president says should be unchanged."
https://news.google.com/newspapers?...aAcsAAAAIBAJ&sjid=e8gEAAAAIBAJ&pg=708,2192714 In short, this would be a vice presidency in name only--and even the name was obviously objectionable to both Ike and Nixon.