The head of the U.S. Postal Service indefinitely delayed her retirement on Monday, pushing the deadline to find the next postmaster general past the end of the month.

The decision by Megan Brennan comes as stakeholders across the postal universe have issued a variety of demands for the USPS board of governors as it engages in its candidate search. The American Postal Workers Union, which represents more than 200,000 USPS employees, held a rally at the mailing agency’s Washington headquarters on Monday to encourage the board to choose a new postmaster general who will refuse to issue any sweeping cuts to service. APWU, partnering with 83 organizations that make up the Grand Alliance to Save Our Public Postal Service, delivered a petition with 350,000 signatures calling on the board to name a new postmaster general committed to maintaining universal service and blocking any effort to privatize the agency.

The rally came as Brennan was set to step down by Jan. 31, after a 33-year career and five-year tenure as postmaster general. The board of governors announced later Monday, however, that Brennan would remain in the job as it continued its search for replacement. The board is in the midst of a “thorough, nationwide search for a successor” to replace Brennan, who agreed to delay her retirement to “facilitate the search and transition process,” the board said in a statement.

Dave Parternheimer, a USPS spokesman, said there is no date by which the search must be completed, noting only that a “nationwide search is underway” and the governors will make an announcement at the appropriate time.

In a government reorganization plan ordered by President Trump, the White House endorsed privatizing the Postal Service after it gets its financial affairs in order. Brennan has expressed an openness to that idea, though she noted it was not up to postal management to decide.

“Ultimately, it will be for Congress to decide whether the best path to financial sustainability is to preserve the Postal Service status as a government institution focused on our mission of public service, while giving us more authority to meet our responsibilities, or whether a profit-maximizing corporate model is preferable,” Brennan said in 2018.

Mike Plunkett, president of PostCom, an association of large-scale private sector postal customers including Amazon and UPS, said his group was not making any specific demands for the new postmaster general. Instead, PostCom is trusting the board to choose someone who will “make necessary changes” to keep the Postal Service running.

“The main thing is someone who is committed to working with the mailing industry and postal customers,” Plunkett said, noting his organization does not have a specific litmus test. “We want someone who can effectively manage the affairs of the Postal Service and can make improvements to make the network viable for the indefinite future.”

He applauded the board for delaying its decision in order to engage in an “exhaustive search,” and speculated the ongoing headhunting indicates it will choose someone from outside the organization. The last four postmasters general came from within the agency, following a series of outsiders that headed USPS in the 1980s and 1990s.

The Coalition for a 21st Century Postal Service, another association of postal customers like Amazon, eBay and the National Newspaper Association, recently sent a letter to the board outlining its expectations for the next postmaster general. Suggestions included a leader with experience with unions and labor relations, as well as someone committed to delivering mail six days each week and protecting universal service.

“We are looking at this with a sense of commonsense and practicality,” said Art Sackler, who leads to coalition. “What’s needed is somebody dedicated to the mission of the Postal Service, somebody with experience with a very large, labor-intensive organization, someone who is tech savvy and innovative. Somebody with marketing experience would be good and somebody who can really be the public face of the Postal Service.”

While he said the coalition wanted to be careful not to “handcuff” the next postmaster general with specific demands, Sackler cautioned that the forthcoming leader must find a way to right the ship without piling “rate increases on backs of customers who all have alternatives to the Postal Service.” Brennan previously suggested the Postal Service should have full autonomy in setting its prices, though the Postal Regulatory Commission has proposed a more modest path to enable USPS to issue sharper rate increases.

Sackler also predicted the board could select someone with more digital experience than exists within the current USPS workforce. The Alliance for Nonprofit Mailers also suggested the extent of the search indicates the board wants someone external to the agency. That background could provide a lift to the Postal Service, the alliance said, as members of Congress may hold a private-sector-executive-turned-postmaster-general in higher esteem when he or she demands legislative changes to USPS operations. The group rejected the notion that Brennan’s pending retirement signals anything about the direction of the agency or that Trump has undue influence on the agency as a means of carrying out personal feuds.

“With a crisis declared by the two most recent [postmaster generals], and no solution in sight, it makes sense that a new set of governors would want their own CEO to help them turn things around,” the alliance said in a statement. “It’s just common sense—not partisan politics, not an attempt to privatize, and not animosity toward Amazon.com, as some have argued.”