(CNN) -

The Supreme Court on Monday tried to make sense of conflicting standards when determining a key question in workplace discrimination claims: Who is the boss?

In an intense oral argument, the justices raised numerous scenarios to explore when a worker's actions were supervisory in nature but appeared uncertain on what approach was best for resolving the central legal question and whether a clear definition could even be established.

"There are situations where the assignment of [workplace] responsibilities is extremely unpleasant," said Justice Samuel Alito. "But there are also a lot of situations, where it's really very unclear. I don't know how courts are can grapple with that."

In a case closely watched by worker rights groups and business, a university catering employee claimed her work environment was a "living hell" due to the alleged actions of a fellow worker who she claimed was her supervisor even though the woman had no power to hire or fire her.

Maetta Vance was the only African-American in her office at Ball State University and had a long-running rift with white employee Saundra Davis. The matter included allegations of physical confrontations and racial epithets.

Vance filed various complaints with the Equal Employment Opportunity Commission and then sued in federal court, claiming her university kitchen was a "living hell."

The lawsuit argued Davis was a supervisor because she did not have to "clock in" and record her hours like other caterers and had authority in the kitchen to ensure daily tasks assigned by the chef and general manager -- her direct supervisors -- were performed.

But the university said it took corrective action to minimize personal conflicts between the two women, and that Davis did not have direct supervision over Vance and could not fire her.

Federal courts agreed with the university in Vance's case, using a narrow standard of defining a supervisor in dismissing the suit.

A gateway legal issue when first bringing allegations of discrimination or harassment is often figuring out whether the person instigating the wrongdoing is a "supervisor," and what authority that person has over the staff.

The high court has long said liability is automatically triggered when the boss harasses or threatens a subordinate.

If the conduct involves two co-workers with roughly the same duties, no legal action can be taken unless their manager was negligent in allowing the misconduct to continue.

Federal appeals courts are deeply divided over whether a "supervisor" is only someone with the power to "hire, fire, demote, promote, transfer, or discipline" employees as defined by the government; or more broadly, someone with the power to manage the day-to-day activities of colleagues.

During oral arguments, Chief Justice John Roberts wondered whether a senior employee who determined what music his co-workers heard on the job would make him a supervisor.

"That could be far more severe," said Roberts, "than, simply saying, you're going to-- as in this case-- be cutting the celery rather than baking the bread, or whatever."

Alito then jumped in. "What was the most unpleasant thing that Davis could have assigned [Vance] to do? Could it be chopping onions all day, every day?"

Vance's attorney Daniel Ortiz replied "chopping onions all day might be punishment" and could trigger a workplace retaliation or discrimination claim.

But Justice Ruth Bader Ginsburg was blunt.

"Did Davis ever have that authority, because the record as far as we have it says that the work assignment, what Vance was doing, came from the chef or from [general manger], and the most that Davis did was transmit the chef's orders of where people would be stationed."

The Obama administration supports neither side, but Justice Department attorney Sri Srinivasan argued that a person qualifies as a supervisor when he or she controls a subordinate's work activities and subjects that person to harassment.