Has a professional athlete ever been traded twice or more times in the same season?

Lots of times. Mike Piazza and Dave Kingman for example.

Kingman played for 4 teams in 1977 (traded twice)

June 15, 1977: Traded by the New York Mets to the San Diego Padres for Paul Siebert and Bobby Valentine.

September 6, 1977: Selected off waivers by the California Angels from the San Diego Padres.

September 15, 1977: Traded by the California Angels to the New York Yankees for Randy Stein and cash.

I think Piazza played a week with the Marlins before getting traded to the Mets. He started out the season with the Dodgers.

Armando Benitez played for the Mets, Mariners and the Yankees in '03

There's more, but these are the only ones I can remember off the top of my head.

Besides the ones listed above, it has happened already this season.....

This offseason, the Phillies picked up Ronny Paulino from the Pirates. Couple days before the season started, they traded him to San Fran. The other night, Im watching the Phillies game and Paulino is catching for the Florida Marlins.......

Yes, a lot of times.

Todd Ziele played for four different teams in 1998, and was traded twice during that season.