And once the Cardinals eventually determine the when, they'll seemingly have a challenging time figuring out the who. All three could make the case that they are ready for a chance.
"That's great to see," Mozeliak said. "And the fact that the production level is so high from those guys, it really might be who is the best fit at the time.
"For me, the timetable is always fluid. It's about what you may do to try and jumpstart something up here. There is also a point where someone down there, it may just be time to give them that opportunity, and we have to become creative on how to do so. The end game right now is we believe in the players we have on this team, we want to give them some patience to try and go out and show why they're here and why they're on this club originally. For me, it's still about being patient and letting this play out a little bit."
Taveras, ranked as the Cardinals' top prospect by MLB.com, entered Friday having had three consecutive three-hit games. He ranked sixth in the Pacific Coast League with 35 RBIs, and was hitting .465 with runners in scoring position.
In 13 games since being optioned by St. Louis, Grichuk is 20-for-54 with six homers, three doubles, 16 runs and 12 RBIs. Piscotty, who had two doubles on Thursday, is batting .299/.337/.443 with 13 doubles and 26 RBIs this season.
None of the three had played a full season in Triple-A before this season, and it is that point that Mozeliak emphasized when asked if he was concerned about the young outfielders growing complacent if they continue to have success without the reward of a promotion.
"I think the fact that you look at a lot of players' career paths, they have more than 300 plate appearances at Triple-A before they get brought up," Mozeliak said. "I don't think in any way has their development or progress been stalled due to what we have going on there. I think they're pushing each other, frankly."
The Cardinals will play seven straight games in American League parks beginning on June 4, and that could present the organization with an opportunity to summon one of the three and find immediate at-bats, with the designated hitter in play.
Jenifer Langosch is a reporter for MLB.com. Read her blog, By Gosh, It's Langosch, and follow her on Twitter @LangoschMLB. This story was not subject to the approval of Major League Baseball or its clubs.