The pair stepped into the co-captaincy at the back end of last season when Ablett was sidelined for seven games with an injury to his troublesome shoulder.
“Both guys have demonstrated they have the capabilities to lead and drive the team,” Suns coach Rodney Eade said.
“When Gary injured his shoulder last season, we believed they were ready to take the next step and together they took the group to another level.
“That period of time was not only a defining period for them individually, but also the team and it became obvious then, that a co-captaincy model was right for us.”
102-gamer Lynch, who won All Australian honours this year, has long been touted a future AFL captain after he was added to the Suns’ leadership group in 2014.
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May, who’s played 88 AFL games, has a less squeaky clean image on and off the field, having been rubbed out for five matches this year for knocking out Brisbane’s Stefan Martin with a brutal shirtfront.
He served a three-week ban for high contact on Lion’s captain Tom Rockliff in 2015.
Day, a Northern Territorian, was also allegedly involved in a nightclub incident in Los Angeles with former teammate Campbell Brown where he received a broken jaw.