Imagine this scene of workplace harassment, envisioned by Chief Justice John G. Roberts Jr.:

You really hate country music. The senior employee in your office picks the music everyone listens to.

“And the senior employee says . . . ‘If you don’t date me, it’s going to be country music all day long,’ ” Roberts hypothesized.

Roberts and his Supreme Court colleagues on Monday were debating the standards for when a co-worker becomes more like a supervisor and thus opens the company up for damages under federal employment discrimination laws.

Some federal courts have said that only someone who can hire and fire people is a supervisor under Title VII of the Civil Rights Act. Other courts, and the Equal Employment Opportunity Commission, have said that definition is too limiting and that the law should cover those who have the ability to control a co-worker’s daily work activities, regardless of their title or job description.

The distinction is important in employment discrimination law. If a supervisor is creating a hostile work environment or threatening to fire an employee, the employer can be held liable. But if a co-worker does so, the company is liable only if it knew about the treatment and did nothing to stop it.

The court’s decision could greatly expand or restrict the ability of employees to bring harassment complaints. But there were signs during Monday’s argument that the case ultimately may not offer the best vehicle for resolving the question of who is a supervisor because of the disputed facts of the case.

It arises from a poisonous environment among the catering staff at Ball State University in Muncie, Ind. Maetta Vance, an African American, said she was subjected to racial hostility from white co-worker Saundra Davis and others. Davis had some control over Vance’s daily work schedule but had no authority to fire her.

After years of antagonism — Vance said Davis once hit her in the head — Vance filed a lawsuit against the university. But Ball State said there was blame on all sides — Vance had once threatened to shoot a superior, it said — and at any rate, it had done what it could to investigate and deal with each of Vance’s complaints.

The U.S. Court of Appeals for the 7th Circuit upheld a lower court’s decision to throw out Vance’s suit. The appeals court said that since Davis could not fire Vance, she was not a supervisor, and the university was not responsible for Davis’s actions because it had taken corrective action after Vance’s complaints.

Roberts and Justice Samuel A. Alito Jr. said the 7th Circuit’s decision provided courts with a clear line for deciding who is a supervisor and who is not. Roberts and Alito listed a series of workplace actions — such as deciding what radio station to listen to, or setting the thermostat or assigning someone to chop onions all day — that could affect an employee’s daily work life and raise questions about the status of the person making the decisions.

The problem was that all the lawyers addressing the justices — Vance’s attorney, Daniel Ortiz; Deputy Solicitor General Sri Srinivasan, representing the federal government; and even Ball State’s lawyer, Gregory G. Garre — said the 7th Circuit’s definition of who is a supervisor was too restrictive.

All said some version of the EEOC’s view, that the ability to control a worker’s daily activities could qualify someone as a supervisor, seemed right.

Roberts was surprised that Garre agreed. “You have no difficulty, as representing an employer, by saying that in every case an allegation of this sort is made you have to go through a case-by-case description of the particular responsibilities, whether it’s the thermostat, whether it’s the music, whether it’s the assignment of everything that the employee does, and decide on that basis whether or not you should compensate the victim, or whether or not you should go to court?” Roberts asked.

Garre said he felt the court’s precedents compelled his position, but if he is wrong, he would be happy if the court simply upheld the 7th Circuit ruling.

But Justice Elena Kagan made clear she would not agree with that. Kagan, a former dean of the Harvard Law School, noted another example from the “university setting” to reflect her disagreement.

“Professors don’t have the ability to fire secretaries. But professors do have the ability to make secretarial lives living hells,” Kagan said. “So what does the 7th Circuit say about that?

Srinivasan replied, “The professor would not qualify as a supervisor.”

Ortiz said the court should find that Davis qualified as a supervisor and send the case back so Vance could argue her case.

But even Kagan said she was not sure Vance could provide enough evidence that Davis controlled enough of her working conditions to be deemed a supervisor.

And Garre said the university had done all it could.

“Ball State reacted responsibly to the allegations that were made, investigated them and took prompt action where the investigation warranted it, particularly with respect to the most despicable things that were uncovered, racial epithets that were used by another employee,” not Davis, Garre said.

The case is Vance v. Ball State University.