Costa Rican Rebeca Grynspan topped an informal United Nations Security Council vote for the third time on Tuesday, in what appears to be growing momentum for her candidacy to become the organization’s next secretary-general, according to a diplomatic source. Several members of the UN’s most powerful body have expressed a desire for the United Nations to choose a woman as secretary-general for the first time, succeeding Portugal’s Antonio Guterres, whose term expires at the end of December.

Grynspan, a former vice president of Costa Rica who took leave from her position at UNCTAD, the United Nations Trade and Development agency, to campaign for the post, has finished first in three of the four closed-door exploratory ballots held so far. However, a veto by any of the five permanent members of the 15-member UN Security Council could halt her momentum.

On Tuesday, she received 10 votes of encouragement and three negative “discourage” votes, along with two “no opinion” indications, according to the diplomat, who asked not to be identified. The figures confirmed reports published by media outlets specializing in UN affairs.

Former Guyana foreign minister Carolyn Rodrigues-Birkett, who narrowly led the second round of the process, finished second on Tuesday with eight votes of support. Four women and three men are competing to become UN secretary-general. They include Argentina’s Rafael Grossi, the current head of the UN nuclear watchdog, who placed third, followed by Senegal’s Macky Sall, Ecuadorians Ivonne A-Baki and María Fernanda Espinosa, and Uganda’s Olara Otunnu.

There has also been speculation that a compromise candidate could emerge during the process at the request of the five permanent Security Council members with veto power: the United Kingdom, China, France, Russia and the United States. Even if a candidate secures the nine votes required out of the Security Council’s 15 members, that person must also avoid a veto from any of the five major powers, which remain deeply divided.

Once a candidate clears those hurdles, the name is sent to the UN General Assembly, made up of all member states, for confirmation.