This post focuses on the team franchises. From 1931 through 1960, there were eight teams in each league. In 1961 the AL added two new teams and the NL added two in 1962. More teams were added over the years through 1998 resulting in a total of 30 teams, almost twice the original 16. This obviously makes it increasingly difficult for a given franchise to have one of its players win the MVP.
An example of a franchise is the Washington Senators moving to Minneapolis in 1961 and renaming itself the Minnesota Twins. MVP would be considered for that franchise starting in 1931.
Click this link to view all the data, which is from the Lahman database and manipulated using the Microsoft Access database management system (DBMS).
Ten or more:
Almost half the Yankee total comes from three triple winners: Joe DiMaggio, Yogi Berra, Mickey Mantle. The Yanks also had two time MVP: Roger Maris and Alex Rodriguez. Note that half of the prime years of Lou Gehrig and all of Babe Ruth are excluded.
The next fewest to the Indians among the 16 that existed from 1931 through 1960: White Sox 4, twice the Indians.
Among the expansion franchises only two won more than two: Rangers 4, Angels 3, Brewers 3 . The Rangers started as the new Washington Senators in 1961 and the Brewers started as the Seattle Pilots in 1969.
Most cities one team: Braves (Boston, Milwaukee, Atlanta). The Athletics played in three cities but had MVP only in two: Philadelphia and Oakland but not in Kansas City 1955-1967.
Other franchises with MVP in two locations:
Dodgers: Brooklyn, Los Angeles
Giants: New York, San Francisco.
Obviously, the most in a city would be New York: 29. This despite zero for the Mets because of the 20 for the Yankees plus six for Brooklyn (Dolf Camilli, Jackie Robinson, Roy Campanella (3), Don Newcombe) and three for the NY Giants (Carl Hubbell (2), Willie Mays).
The Pirates were 0 for 29 when Dick Groat won the first MVP for them in 1960 but the Pirates now have a total of 7, including three in four years by Barry Bonds.
Giants 5: 2000-2004: Jeff Kent, Bonds, Bonds, Bonds, Bonds.
Yankees 4: 1954-1957: Berra, Berra, Mantle, Mantle
Yankees 4: 1960-1963: Maris, Maris, Mantle, Elston Howard.