All three played a pivotal role in the run to last season’s Championship Shield final, and were involved in Sunday’s pre-season friendly against Doncaster.
Yere, the Eagles’ record try scorer, has been with the club since 2008 and played in the back-to-back Championship Grand Final successes in 2012 and 2013.
Compatriots Lo and Mexico both joined the club in 2016, and director of rugby Mark Aston has outlined a big role for all three of them next season.
“These lads will be a major part of what we are looking to do at Sheffield Eagles going forward,” he said.
“Menzie has been with us for what seems like forever. He is Sheffield Eagles through and through, so to have him with us for another season is great news for the club.
“Through his experience he has a positive influence on Garry and Mark because he has been doing what he does long before they made their mark in the game.
“Menzie still has plenty to offer, and we are delighted to have him.”
Last season Lo showed glimpses of immense talent, but injury restricted his appearances at the start and end of the campaign.
Mexico endeared himself to the supporters last season, carving out a reputation as a fans’ favourite, with Aston adamant that they have plenty more to offer the Eagles.
“Garry scores tries, that’s what he does, and if we can keep him fit we know there will be an end product,” Aston added.
“There were a lot of rumours surrounding Mark maybe leaving the club, but that’s all they were. In my mind there was never any doubt that he would be here.
“Both have enjoyed a good break. They have come back and are ready for the 2017 season.”
Last season winger Lo scored 12 tries in 15 appearances in all competitions for the Eagles, whilst prop forward Mexico scored four tries in 31 appearances.
Centre Yere scored 20 tries in 30 appearances.