Red Sox interim manager Chad Tracy returned to Fenway Park after Monday’s off-day with several promising injury updates to share.

Roman Anthony continues to swing, and on Tuesday took overhand batting practice in the cage for the first time.

Tracy called it “another step in the right direction” for Anthony, but said he didn’t have an answer when asked how many steps the young outfielder must clear before he can begin a rehab assignment. Next steps would include hitting on the field and off a higher-velocity machine, and off the Trajekt, which replicates real major league pitchers’ pitches.

“He’s doing well,” Tracy said of Anthony. “I think you’re still in the phase of like, introducing new things to him, and make sure that you clear those and nothing pops up with the hand. So he’s going to have to do that. … Now, how long all that takes? Like, I don’t know the answer to that yet. But as long as he’s feeling good, we can keep moving him along.”

Garrett Crochet resumed throwing on Monday for the first time since late May. Tracy cautioned the left-hander is only in the “very infant stages” of a throwing progression, just out to 50-60 feet, but said “he’s got a chance, for sure” of returning this season.

Tracy said Trevor Story is “getting closer” to going on a rehab assignment. The veteran shortstop was seen doing early work on the field with injured newcomer Curtis Mead, who suffered a left wrist fracture on a hit-by-pitch in his second at-bat for the Red Sox last Monday.

“He’s continued to track very well, and we’ll just keep tracking him during the course of this week, and see where he’s at as we get towards the end of this homestand, and go from there,” Tracy said of Story, who last played May 14 before undergoing sports-hernia surgery.

Right-hander Tanner Houck is “still doing very well” and is throwing multiple 40-plus pitch bullpens per week at the team’s Fort Myers, Fla. complex. Houck underwent Tommy John surgery, which typically carries a return timetable of 12-18 months, last August. He is “creeping closer to facing hitters,” and over the weekend Tracy said there is a chance Houck could contribute to the big-league team down the stretch.

Fellow righty Kutter Crawford is still “hit and miss” with throwing after suffering another setback, and is “still a ways off.”

Utility infielder Isiah Kiner-Falefa is “doing stuff off the tee, swinging pretty intently,” but still no timetable for his return.

“Nothing new” on first baseman Triston Casas, who underwent season-ending knee surgery last May, then suffered first rib, then wrist setbacks this year when he attempted to begin a hitting progression. Casas was scheduled to see doctors Tuesday, Tracy said.

There’s no timeline on trade deadline addition Adley Rutschman, who went on the injured list with left wrist inflammation in July, but he began a hitting progression over the weekend. He and Tracy both noted they would have more information after meetings with the team medical staff and trainers.