Alvarez is out of the lineup for Sunday's game against the Giants.
The Mets optioned Yan to Triple-A Syracuse on Sunday.
Naylor is starting behind the plate and batting ninth Sunday against the Reds.
May did not factor into the decision in Saturday's 5-3 loss to the Reds, allowing two runs on five hits and no walks with five strikeouts over 3.2 innings.
Thornton (3-5) took the loss Saturday, coughing up six runs on seven hits -- including four home runs -- and a walk over five innings. He struck out six.
Turang isn't in the lineup for Saturday's game against Cincinnati.
Bauers isn't in the lineup for Saturday's game against the Reds.
Stock allowed one hit and retired the other batter he faced while working out of the bullpen in Friday's 10-6 win over the Giants.
Turang went 3-for-4 with a double, two runs scored and three RBI in Friday's 10-7 win over the Reds.
Drohan didn't factor into the decision in Friday's 10-7 win over the Reds, surrendering six runs on five hits and two walks over four innings. He struck out five.
