In their two previous bouts, Mr Levy shamed Mr Netanyahu into creating a grandiose Ministry of National Infrastructure for the steamrolling ex-Defence Minister, Ariel Sharon. This time he is fighting for himself - and a role for the Foreign Ministry.
Like other prime ministers before him, Mr Netanyahu wants to run his own foreign policy, and above all his own dialogue with the Arab neighbours. He contends that as Israel's first directly-elected Prime Minister, he has every right to do so. "I was elected to lead," he told an Israel Television interviewer on Tuesday, "and I intend to lead."
It is his leadership manner that has upset Mr Levy and the Foreign Ministry professionals. Mr Netanyahu, it seems, is cutting them out of the loop. He is proposing to appoint his own man to head the negotiating team with the Palestinians, previously a Foreign Ministry preserve.
Last month he sent his diplomatic trouble-shooter, Dore Gold, a right- wing academic, to Washington for talks with the Secretary of State, Warren Christopher, behind the back of the Israeli embassy. Dr Gold has also visited sundry Gulf capitals without informing the Foreign Ministry. This Monday, the Prime Minister went to Amman at the head of an imposing delegation of advisers and business leaders, but invited neither Mr Levy nor any of the Foreign Ministry brass to join them. Instead, he introduced Mordechai Kristal, an assistant to Dr Gold, as "head of the Jordan division". And on Tuesday he boasted that there was "only one Prime Minister".
That was the last straw. That night, Mr Levy unplugged his telephone and left Jerusalem for his home in the Jordan valley town of Beit She'an. Yesterday, unconvinced by promises to let him "participate", he boycotted two inner cabinet sessions amid hints of resignation.
He was reported to be "consulting" his four colleagues in the Gesher parliamentary bloc, which ran for election in harness with Mr Netanyahu's Likud party, but retained a separate identity. "Levy is upset," one of his confidants told reporters. "He is angry and hurt. He will not allow Netanyahu to take him for a ride."
Experienced Levy-watchers doubt whether he will resign. But his revolt is part of wider discontent, among ministers and Likud MPs, with Mr Netanyahu's presidential aspirations.
"With his own mouth," Nahum Barnea, a widely-read columnist, wrote in the tabloid Yediot Aharonot yesterday, "Netanyahu has transformed his ministers into the opposition. David Levy now joins Ariel Sharon, and others will flock to them. They cannot overthrow the Prime Minister, but they can make his life miserable."