In 1975, in the wake of Watergate, Congress began investigating the CIA. President Ford, a former VP replaced the CIA director with George H.W. Bush (a future VP.) Also, to head off the congressional investigations he assigned his own VP, Nelson Rockefeller, to head a committee. Reportedly the White House chief of staff orchestrated these moves. In the case of Rockefeller he was trying to weigh Rocky down with committee work so he couldn’t get anything done as the chair of the Domestic Policy Council. Rumsfeld had also brough Bush into the CIA to hurt his future political career – Rumsfeld harbored presidential ambitions of his own. Decades later Rumsfeld’s machinations were remembered and his appointment to Defense was not a popular move amongst the Bushies.
But Rumsfeld had an important ally in the Bush 43 administration. His old deputy and successor at the Ford White House, future VP Dick Cheney.
I can think of several points where two past, future & present VPs worked together (any where the President had been VP for starters) but FOUR on one particular issue must be some sort of record.