Among those possibilities, looms the fairytale notion that Zach Johnson could win his favourite tournament again at age 50.
Hodges had four birdies in a six-hole stretch on the back nine of the TPC Deere Run for a 67 to join fellow American Glover at 16-under 197 going into Sunday's final round.
Nine players were within four shots of the lead, a group that ranges from Johnson to NCAA champion Preston Stout of Oklahoma State.
Glover's three-year exemption on the PGA Tour from winning twice in 2023 expires this year, and he began the season still recovering from labrum surgery.
"You pretty much know you've got to go low or you're not going to win," Glover said. "Everybody is going to have to be aggressive, so I've got to hit it a little better tomorrow to achieve the ultimate goal."
Hodges hit his stride on the back nine, with six consecutive holes leaving birdie chances of 15 feet or closer. He converted four of them to join Glover. But there is little room for error.
Zac Blair (67), Ben Kohles (66) and Jackson Suber (66) were one shot behind. Another stroke back was Doug Ghim (67).
Still lurking three shots behind was Johnson, who has such a strong history at the John Deere Classic that he skipped the US Senior Open at Scioto this week.
Johnson captured the title in 2012 and has recorded numerous top-five finishes in the event.
He poured in a 35-foot birdie putt on the last hole for a 66.
Johnson will have a chance to join a small group of players to have won on the PGA Tour Champions and the PGA Tour in the same calendar year. Phil Mickelson was the most recent in 2021.
Stout, playing on a sponsor exemption, shot 66 and was in the group four shots behind that included Max Homa and Ryo Hisatsune.
The lone Australian in the field, Karl Vilips, posted a 68 to be tied for 47th, eight shots from the lead.
