Anthony has been out since May 4 with a partially torn tendon in his right ring finger. He struggled at the plate over the first 30 games of the season, logging a .675 OPS with just one home run.
The 22-year-old sophomore does have two home runs and a 1.023 OPS over seven rehab games split between double-A Portland and triple-A Worcester.
Last year, Anthony missed Boston’s wild-card series against the Yankees after sustaining an oblique strain.
Story has been out since May 14 with a sports hernia injury. The veteran shortstop also struggled with three homers and a .547 OPS over the first 41 games.
The 33-year-old had 25 home runs and 96 RBIs last season but averaged only 54 games over the previous three years.
Meanwhile, the Red Sox have thrived despite their injuries. After struggling to start the season and firing longtime manager Alex Cora on April 25, Boston went on a 32-5 run, including a franchise-record-tying 15-game winning streak, to surge back into the post-season picture.
Now they’re close to adding two more bats to an offence that has scored the most runs in the American League in August as they push towards October.