“Why can’t white people and black people just get along?” Jaclyn asks her boss, who is secretly trying to get her fired. That this question remains so current surely explains how “Rasheeda Speaking” was able to attract such a first-rate team — it marks Cynthia Nixon’s directorial debut and stars two other remarkable actresses, Tonya Pinkins and Dianne Wiest.

They play two office workers for a Chicago surgeon, Dr. Williams (Darren Goldstein, who also portrays the schmucky diner owner in Showtime’s “The Affair.”) As the play begins, Dr. Williams is enlisting Ilana (Wiest) to spy on Jaclyn, so that he can build up a case to convince Human Resources at the hospital to have her fired. Why does he want to get rid of her? “I don’t think she fits in, I don’t think her work is very good.” and “She seems unhappy.” And: she has an attitude problem.

Ilana, mousy and loyal and easily intimidated, clearly feels she has no choice but to comply, even though she likes Jaclyn, who is much more outgoing. But Jaclyn quickly figures out what’s going on, and executes a plan to protect her job and exact her revenge.

That, at least, is a description of how the play is surely supposed to unfold. But the characters’ actions are not as crisp and their reactions are not as credible as they are clearly intended to be.

Playwright Joel Drake Johnson, who is white, was reportedly inspired to write “Rasheeda Speaking” after an unpleasant encounter he had with an African-American receptionist at a hospital; he wrote a letter of complaint about her, and she was fired. He wanted to bring to life a story from her point of view, and presumably to explore the latent racism that plays a part in everyday encounters.

This is a worthwhile subject, and there are both funny and thought-provoking moments in the play:  Dr. Williams complains to Ilana that Jaclyn doesn’t look him in the eye, for example, and later Jaclyn has the same complaint – that Dr. Williams doesn’t look at her.  Setting it in an office is an especially smart choice; it’s in the workplace where people of different races are most likely to interact with one another on something approaching an equal basis.  But the exaggerated attitudes and behavior of all four characters count as a missed opportunity to explore the more usual, more subtle, if no less insidious dynamics of race relations. A patient (Patricia Conolly) reacts against Jaclyn’s rudeness towards her by citing without rancor her son’s belief that this is part of Jaclyn’s culture – “your way to get revenge for slavery.”  Jaclyn is not just rude; she’s also weirdly mean and manipulative (she deliberately rearranges the contents of all of Ilana’s desk drawers, trying to make her believe that she herself has simply forgotten she’s done this.) She is also herself a bigot against her Mexican-American neighbors. Ilana becomes so frightened of Jaclyn that she brings a gun with her, on the advice of her husband.

These characters could be dismissed as not just implausible, but cloddishly drawn, if it were not for the stellar cast.

Rasheeda Speaking

The New Group at Pershing Square Signature Center (480 West 42nd St.)

By Joel Drake Johnson; directed by Cynthia Nixon; sets by Allen Moyer; costumes by Toni-Leslie James; lighting by Jennifer Tipton; music and sound by David Van Tieghem.

Cast: Patricia Conolly (Rose), Darren Goldstein (Dr. Williams), Tonya Pinkins (Jaclyn) and Dianne Wiest (Ileen).

Running time: 95 minutes with no intermission.

Rasheeda Speaking is scheduled to run through March 22.