Edwin Jackson
Teams played for: Dodgers (2003-2005), Devil Rays/Rays (2006-2008), Tigers (2009; 2019), Diamondbacks (2010), White Sox (2010-2011), Cardinals (2011), Nationals (2012; 2017), Cubs (2013-2015), Braves (2015), Marlins (2016), Padres (2016), Orioles (2017), Athletics (2018), Blue Jays (2019)
Potential 1% combos: Jackson played for more MLB teams than any other player. It's a good thing for all the team combos, but the 1% combinations are the teams he threw the least amount of innings for.
Braves/Orioles, Braves/Marlins, and Braves/Blue Jays will be your best bets.