Discovering how to make a sensitive subject sing is a tricky business. Just ask Angelica Chéri and Ross Baum, who wrote more than 90 songs in their search for the proper tone for “Gun & Powder,” their exhilarating musical about black twin sisters who break man’s laws to find the spiritual ones they can live with.

The inspired songwriting team, unveiling the results in a marvelously sung world premiere at Signature Theatre, have settled on about two dozen numbers — and a show traversing the rich and rocky terrain of American biracial identity. It’s a musical about having the right to choose who you want to be, in a country so riven by tribalism that improvising a new racial persona can seem the most subversive act imaginable.

Librettist-lyricist Chéri and composer Baum, along with director Robert O’Hara, use a mix of jazz, blues and soul to infuse the story of Mary and Martha Clarke — portrayed magnetically by Solea Pfeiffer and Emmy Raver-Lampman — with electricity and wit. They’ve made psychologically persuasive Chéri’s own family legend: the story of her light-skinned ancestors, who, in the Texas of 1893, find in passing for white a conveyance for a lucrative life of crime.

The creative team’s task is not at an end though, despite some exemplary support, both from costume designer Dede Ayite and such actors as Awa Sal Secka and Yvette Monique Clark, who play gossipy housemaids who catch on quickly and amusingly to the sisters’ masquerade. For although “Gun & Powder” builds efficiently to a climax in Act 1, the musical suffers from a fairly common problem in musical-theater development: an Act 2 that drains some of the evening’s estimable power.

Chéri and Baum pack in so many thematic possibilities that the dramatic thrust becomes a bit muddled; like the sisters themselves, an audience loses track of where we’re headed. What is it that Mary and Martha want, exactly? Why does their run from the law not feel more desperate? How has turning into bandits changed them? And if pretending to be white is more than their ruse, what is the grander ­epiphany?

Most curious is awarding the production’s precious slot, the penultimate song (or, in theatrical parlance, the “11 o’clock number”), to a character of only tangential interest: the bigoted white man whom Mary has married over Martha’s violent objections. Jesse (Dan Tracy) comes across as a device more than a match for Pfeiffer’s elegant Mary, who more than Martha is intoxicated by the advantages of eschewing her blackness.

His song, “Even Human,” documents his turmoil over Mary’s disclosure of her true identity. The problem can be summed up in two words: Who cares? “Gun & Powder” up to this point has been focused chiefly on the survival of Mary and Martha, and their efforts to obtain money to help their mother, Tallulah (the excellent Marva Hicks). The state of Jesse’s mind ranks low on a spectator’s priority list, especially at this late juncture.

So much of “Gun & Powder,” though, remains fresh and exciting. The story, as O’Hara’s vivacious ensemble informs us, is based on a legend — the folklore, in fact, passed down in Chéri’s own family. Mary and Martha Clarke were real, but their exploits are fully fictionalized. What’s vital in “Gun & Powder” is the profound transformation Mary and Martha undergo by an utterly superficial ruse. Leaving the homestead of their destitute sharecropper mother, who’s dependent on the white landlord from whom she leases land, the young women decide that appearing white themselves, the genetic bequest of their absent white father, is too big an advantage to pass up.

Chéri and Baum send up the sisters’ new status in the acerbic “Just Passing Through.” On a Texas train, they mingle with white passengers whose mindless conversation has no intrinsic meaning for them: “Something cup of tea/ Something honeybee/ Something and a big magnolia tree,” we hear one passenger sing. While the intermittent romantic interludes seem garden variety — the supple-voiced Donald Webber Jr. portrays an earnest servant who falls in love with Martha — the efforts to introduce racial duality into the musical are clever. In one such number, “Frenchman Father,” a white saloon singer (Crystal Mosser) turns a facsimile of the Clarkes’ own history into a shameless burlesque. We see just how cavalierly the white world treats black identity.

O’Hara, a playwright himself, who recently directed the hilarious, button-pushing “Slave Play” on Broadway, has a penchant for illuminating political realities through comedy; when “Gun & Powder” allows us to see where and how the trials of black women in 1893 led us to 2020, the musical is at its entertaining best. And best, too, when we’re in the heads of Peiffer’s and Raver-Lampman’s Mary and Martha, contemplating the new horizons they may someday be able to see.

Gun & Powder, book and lyrics by Angelica Chéri, music by Ross Baum. Directed by Robert O’Hara. Music direction, Darryl G. Ivey; choreography, Byron Easley; sets, Jason Sherwood; costumes, Dede Ayite; lighting, Alex Jainchill; sound, Ryan Hickey; orchestrations, John Clancy. With Amber Lenell Jones, Rayshun LaMarr, Christopher Michael Richardson and Kanysha Williams. About 2½ hours. $40-$85. Through Feb. 23 at Signature Theatre, 4200 Campbell Ave., Arlington. sigtheatre.org.