The Orleans Parish School Board is gearing up for Round 2 in the search for its next permanent superintendent, Round 1 having served mainly to weed out an initial crop of candidates in a hunt that’s been going on for the better part of two years.

The board interviewed an initial group of four finalists in March, but it never voted to bring any of them back for another talk. That would normally have been the next step toward finally replacing Stan Smith, who has served on an interim basis since mid-2012.

Now, after more than a month without any news on the status of the search, board President Nolan Marshall Jr. said he hopes to schedule another round of interviews with fresh candidates late this month, probably May 22 if all board members can attend.

“There have been more applications and ongoing conversations with people who are interested,” Marshall said. “We’re in various stages with various candidates.”

For the board to be contemplating a whole new group of hopefuls at this point may signal one of two things: that board members are determined to take their time in carrying out what many have described as their most important job, or that an often-divided board cannot agree on the qualities the members want in a new leader. Ultimately, both factors may be involved.

Whatever the case, it may be some time before there is another slate of finalists for the public to get a look at.

Bill Attea, of the search company Hazard, Young, Attea & Associates, said his firm is continuing to vet candidates as they come up, but it hasn’t settled on another list of names to forward to the board.

In part, he said, that’s because the company still isn’t sure what criteria board members want to prioritize.

As he unveiled the first four finalists in March, Attea pointed out that some of the qualities board members said they wanted in a candidate contradicted one another.

“The criteria last time were a very long laundry list,” he said. “We’re still trying to respond to everyone’s preferences. They have to be narrowed a little further, and that’s what we’re trying to do. The more focus you can provide, the greater the possibility of finding someone the board is going to like.”

Toward that end, Attea said he will be trying to reach out to board members before drawing up another list of names.

The last group of candidates proved to be a diverse and mainly untraditional set of potential leaders, including two from New Orleans and two from out of town. They were a local school leader, a lawyer who sits on the board of a local charter school, a former school district administrator from Philadelphia and a superintendent from the British territory of Bermuda.

Two of them — Kyle Wedberg, president of the New Orleans Center for Creative Arts, and Edmond Heatley, Bermuda’s education commissioner — pulled their names from consideration after the first round of interviews.

Whoever gets the job will lead a nontraditional district, to say the least.

Having lost most of the city’s public schools to the state-run Recovery School District after Hurricane Katrina, the local School Board oversees a much-diminished system, made up chiefly of independent charter schools that make their own decisions on hiring, curriculum and other matters.

For now, it’s still unclear when — if ever — the city’s public schools will come back under one unified governing body again, leaving considerable uncertainty for any future leader.