Nassau Community College trustees will again return to their presidential-search applicant pool and also will consider more candidates in the nearly four-year quest for a permanent leader for the school, a State University of New York official said Wednesday.

Johanna Duncan-Poitier, senior vice chancellor for community colleges, told Newsday that SUNY is working very closely with NCC’s board of trustees to consider “additional candidates they have not looked at before.”

“The priority is that we get the right candidate,” Duncan-Poitier said when asked how long the Garden City school may be without a permanent president. “We want strong leadership and we are working on that immediately . . . We are looking at very specific leadership skills in light of the Middle States report — it is that serious.”

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A team from the Middle States Commission on Higher Education, which accredits the college, issued stinging feedback in an oral report last month after a three-day campus visit, finding the school had fallen out of compliance with half of the accrediting agency’s 14 quality standards. That report changed the nature of the presidential search, Duncan-Poitier and others have said.

Among the areas the review team found lacking were stable leadership, integrity, planning and financial resources. Middle States is due to issue a written report next week.

Duncan-Poitier’s comments came the day after NCC trustees, at their regularly scheduled meeting Tuesday night, did not nominate a candidate for president from two remaining finalists. Board members had been tasked with interviewing the two and selecting one of them after their initial choice, longtime NCC administrator and current executive vice president Kenneth Saunders, withdrew from the search.

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Instead, after more than three hours behind closed doors on Tuesday with Duncan-Poitier, trustees resumed the public portion of the meeting without having nominated a candidate. SUNY Chancellor Nancy L. Zimpher must approve any president chosen by the board.

“After executive session, we would like to report that the decision on the position for permanent president of Nassau Community College was not reached,” said trustee Arnold Drucker, co-chairman of the search committee. None of the trustees would comment on the outcome of the meeting.

The remaining finalists were Tyjaun A. Lee, 44, vice president for student services at Prince George’s Community College in Largo, Maryland, and Stephen Schoonmaker, 57, former president of the College of the Ouachitas in Malvern, Arkansas.

It was unclear after the meeting whether those finalists would continue to participate in the search. Neither could be reached for comment Wednesday.

Three times since mid-2012, search committee members have narrowed the applicant pool to a handful of finalists for trustees to interview and select for state approval. Controversy over bias, favoritism, political influence, candidate withdrawals and faculty dissent have kept efforts from moving further.

The institution, with about 22,000 students, is the largest single-campus community college in the SUNY system.

Thomas Dolan, former superintendent of the Great Neck school district, is Nassau Community College’s current interim president. Duncan-Poitier on Wednesday declined to comment on whether Dolan or any other administrator at NCC could be considered as an applicant in the presidential search.

The president’s post at NCC has been vacant since Donald Astrab, who got two votes of no-confidence from faculty during his 36 months on the job, left in July 2012.

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In August 2012, trustees appointed Saunders, 59, of Freeport, then the college’s executive vice president, to lead the school. As acting president, at a salary of $225,000, he was a finalist in two presidential searches.

Saunders was the presumed front-runner and the choice of NCC trustees at their March 3 meeting, but received two votes of no-confidence from the college’s unionized faculty and its academic senate.

On March 23, a spokeswoman for SUNY told Newsday, “The candidate sent forward by the Nassau Community College board of trustees has withdrawn from consideration.”

Richard Pokrass, spokesman for the Middle States Commission on Higher Education, said Wednesday he is not sure if the prolonged presidential search could affect the college’s reaccreditation.

“The commission is aware of the presidential search at Nassau and it is too early to tell whether the current situation would enter into the discussion on the college’s accreditation status,” Pokrass said.

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Last month, after the review team’s visit, Pokrass said NCC’s accreditation status would remain unchanged until any possible action the commission might take at its June 23 meeting.