Patti LuPone and Christine Ebersole — both Broadway divas, both two-time Tony winners, and both of whom gave a performance of a lifetime a decade ago (LuPone in “Gypsy,” Ebersole in “Grey Gardens”) — now come together to portray the dueling cosmetics queens Helena Rubinstein and Elizabeth Arden in the messy but smart and rousing new musical “War Paint.”

Imagine a sequel to “Wicked” where the two young witches of Oz have grown up to become middle-aged businesswomen in early 20th century New York.

Inspired by a dual biography that subsequently became a PBS documentary, the musical begins in the early 1930s, at which point both women (who came from very different backgrounds) have already achieved fame and fortune selling women’s beauty and health products.

Legend has it that they never met in person but were obsessed with each another. Nevertheless, the authors of “War Paint” (book by Doug Wright, music by Scott Frankel, lyrics by Michael Korie) come up with various ways to have both appear onstage simultaneously (including a dreamed-up final reconciliation scene).

Rubinstein and Arden scheme to outdo each other, adapt to societal changes (including FDA regulations and World War II supply shortages) and steal each other’s male business companions (played by John Dossett and Douglas Sills), until both are outmatched by Charles Revson (Erik Liberman) and his Revlon brand, with its glitzy television advertising and direct appeal to younger women.

The musical is built around an unwieldy and repetitive Ping-Pong structure of shifting back and forth between the two characters. It’s not impossible for a musical to build a coherent storyline while exploring two historical rivals (i.e. Hamilton and Burr in “Hamilton”), but at least those two fought face to face (both with words and pistols).

However, “War Paint” still has a lot going for it, including self-empowered protagonists, high-powered performances, well-crafted period-style songs, the classy aura of old-school New York and the smooth direction of Michael Greif (who staged “Dear Evan Hansen” earlier this season).

It ought to be a hit with Broadway’s primary ticket-buying demographic: women from the tristate area who use cosmetic products, are familiar with Rubinstein and Arden’s important legacies and know that LuPone and Ebersole are musical theater artists of the highest caliber.