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In a last-minute game of musical chairs on Broadway, the revival of “The Caine Mutiny Court-Martial” will shift from the Lyceum to the Schoenfeld, clearing the way for a transfer of the Off Broadway hit “The Lieutenant of Inishmore” to open at the Lyceum before the Tony deadline.

Move snaps into place the final pieces of a jam-packed season in which Broadway houses are at a premium. The next tenant of the Schoenfeld had been a hot topic along the Rialto ever since “Chita Rivera: The Dancer’s Life” shuttered there Feb. 19.

The limited run of “Caine Mutiny,” starring David Schwimmer and Tim Daly, fits well into the Schoenfeld’s slate, with a revival of “A Chorus Line” set to start previews there Sept. 18 for an Oct. 5 opening.

The original Broadway production of “Caine” preemed at the Schoenfeld in 1954, when the venue was called the Plymouth. The revival starts performances April 14, with opening May 7.

Atlantic Theater Company’s production of “Inishmore,” the black comedy by Martin McDonagh (“The Pillowman”) won critical raves when it opened earlier this week, spurring commercial producers Randall L. Wreghitt and Dede Harris to make swift plans for an uptown transfer.

The Atlantic’s last team-up with McDonagh, “The Beauty Queen of Leenane,” moved to Broadway and took home a handful of Tonys in 1998. “Inishmore,” which closes at the Atlantic April 9, will begin performances at the Lyceum April 18 and open May 3.

Another potential tenant at the Schoenfeld, MTC’s production of Conor McPherson’s “Shining City,” is staying put at the Biltmore rather than moving to allow a further extension of the Biltmore’s current, strong-selling tenant, “Rabbit Hole,” starring Cynthia Nixon and Tyne Daly.

To accommodate a “Rabbit Hole” extension through April 9, “Shining City” has pushed back its dates a week, now starting perfs April 20 and opening May 9.