WI Vice President in Cabinet?

In the Philippines, the VP can simultaneously be in the Cabinet. What if the US adopted an amendment to allow this? If you want, you can name post WWII VP's in OTL and their possible portfolios.

Alben Barkley (1949-1953): Secretary of Agriculture
Richard Nixon (1953-1961): Secretary of State (1959-1960)- In OTL it was considered, but Nixon didn't want to lose hammerlock on '60 nomination.
Lyndon Johnson (1961-1963): ?
Hubert Humphrey (1965-1969): Secretary of Commerce
Spiro Agnew: (1969-1973): HUD Secretary (valued for suburban wisdom)
Nelson Rockefeller (1973-1977): Treasury Secretary
Walter Mondale (1977-1981): Secretary of Agriculture
George H.W. Bush (1981-1989): ?
Dan Quayle (1989-1993): Commerce
Al Gore (1993-2001): HUD Secretary
Dick Cheney (2001-2009): Secretary of Defense
 
um, there's nothing in law against the VP being in the Cabinet, it's never been done because each Cabinet leave job is thought of as full time job (24/7)

any ways
George H.W. Bush (1981-1989): Director of Central Intelligence
 
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