Twice in the past six years, the museum’s troubles became so acute that proposals were floated to merge it with the Los Angeles County Museum of Art, its larger neighbor to the west. At the urging of Mr. Broad, the museum also explored an agreement last year with the National Gallery of Art in Washington that would have involved collaborations on programming and research but not a merger.

As the museum looks ahead to try to stabilize itself, Maria Arena Bell, who is stepping down after the end of her term as a co-chairwoman of the museum’s board, said in an interview Monday that there were “absolutely no plans” being discussed by the board for the museum to share curatorial, administrative or any other significant resources with the Broad, the private contemporary art museum that Mr. Broad and his wife, Edythe, plan to open next year almost directly across the street from the main site of the Museum of Contemporary Art on Grand Avenue in downtown Los Angeles. While the two museums might collaborate on marketing strategies and have a “very friendly relationship,” she said, they will remain separate entities. Ms. Bell added that there were no strings attached to any of the donations or pledges that would require the museum to join forces in any way with the Broads’ museum.

Even as it began to shore up its finances recently, the museum endured three rocky years under the leadership of Jeffrey Deitch, a veteran New York art dealer whose selection as the museum’s director in 2010 was highly unconventional. While his tenure included a few well-attended, critically praised exhibitions, it suffered from staff defections, budget problems and the departure of all four artists on the museum’s board; the artists complained that Mr. Deitch was taking the museum too far away from serious shows and toward celebrity, fashion and pop culture. After Mr. Deitch resigned in 2013, during the third year of a five-year contract, the four artists — John Baldessari, Catherine Opie, Barbara Kruger and Ed Ruscha — joined the search committee for a director. (Mr. Deitch said on Monday that he was “looking for a large space in New York where I can present ambitious projects.”)

David G. Johnson, the museum’s other co-chairman, who is also stepping down after many years on the board, said that none of the donations or pledges for the endowment were contingent upon Mr. Deitch’s leaving. He added that the museum remained “committed to continuing both a program of diverse artists and diverse audiences.”

But in its search for the next director, Mr. Johnson, Ms. Seferian and Ms. Bell added that the candidates considered have been museum professionals, not figures from the commercial art world or from other nonprofit institutions. A director will probably be chosen in the next few weeks, the officials said.