Flaherty (shoulder) will throw another bullpen session Tuesday, Jeff Jones of the Belleville News-Democrat reports.

It will be the righty's third bullpen since beginning his throwing program, so a progression to facing live hitters seems likely if he avoids any setbacks. Flaherty has little chance of returning in his normal starting role this regular season, but his availability in any capacity could be huge for the Cardinals as they battle for the second wild-card spot.

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