This kind of scenario happens all the time.
Go back to 1997 for a minute. The Minnesota Twins dealt All-Star second baseman Chuck Knoblauch to the New York Yankees for Christian Guzman, Eric Milton, Danny Mota, and Brian Buchanan.
Eric Milton, who was an All-Star and pitched a no-hitter for the Twins, was traded to Philadelphia for Carlos Gomez and Nick Punto.
Brian Buchanan was traded to the San Diego Padres for Jason Bartlett, who was then sent to Tampa Bay for Delmon Young and Brendan Harris.