Art auctions used to be a gentlemen’s business. Now the gloves are off.

As art sales face their first major test since the August financial market rout, auction houses are jockeying not only for trophy artworks but also for the best positions to highlight them at the November auctions in New York. The result is a shakeup in a schedule that for years was tightly coordinated, with Christie’s and Sotheby’s traditionally alternating who goes first. Even the weekends are no longer off limits; in a surprising move, Phillips, the smallest of the three, switched its main sale to a Sunday.