Back in November, the personal animosity among top members of the White House staff had become so intense it seemed nearly certain that some Reagan team members could not survive.

One faction--chief of staff James A. Baker III, deputy chief of staff Michael K. Deaver and presidential assistant Richard G. Darman--was seen as pushing for the ouster of White House counselor Edwin Meese III, a long and trusted friend of Reagan and his most ideologically conservative senior aide.

Meese's faction, in turn, identified Darman as a troublemaker and spread stories that he was "not a real Reaganite," presumably because of his past association with moderate Republican and former Nixon Cabinet member Elliot L. Richardson.

Still another group of White House aides, some of whom thought Baker was exhausted and Meese poorly organized, wanted national security adviser William P. Clark, who has known Reagan since his 1966 campaign for California governor, to take over as chief of staff.

What happened, said Deaver, is that President Reagan made clear that he didn't want any of these things to happen. He did not want any change at all.

"Reagan doesn't believe anything bad about anyone working for him," added another White House official. "And that includes the staff, which is why he doesn't pay attention to the friction. He talks about these grown men working for him as 'the boys.' He says, 'I think the boys are all right.' "

There are many others in the administration who don't agree with the president. They point to a number of instances in which the staff appears to have dropped the ball, including the hastily withdrawn proposal to cut Social Security benefits in 1981, and the ill-fated policy option disclosed last Thanksgiving to tax unemployment benefits.

Even more significant, said some officials, are the inhibitions to change created by a system with four competing power centers. It is difficult to make personnel changes because three people--four in the foreign policy field--have a veto. The system of shared power makes it difficult to pinpoint responsibility when something goes wrong.

"The system protects all of them," said one White House official. "It frustrates them and it protects them. When things don't work, they hide behind the system."

But whatever the system's strengths and weaknesses, administration officials agree on one important point: The White House is organized the way Reagan wants it to be. If it wasn't, said Meese, he would change it.

"Were all of us to leave tomorrow for the private sector, were Reagan to get an entirely different team, he would create one like we have now," said White House communications director David R. Gergen, who also observed that the president is comfortable with the system and "is not terribly caught up in the organization problems of the White House."

Those who have known Reagan a long time attribute his preference for a diffused leadership with rival power centers to a need for "implementers" to balance his ideological bent, his background as a Hollywood actor who responded passively to the commands of directors and producers, and his past disappointments with a "strongman" chief of staff early in his California governorship and a "strongman" campaign manager early in the 1980 presidential race.

Whatever the reasons, Reagan has repeatedly made it clear--especially to his closest aide, Deaver--that he does not intend to put one man in charge and let him run the White House as many other presidents have done. "There was a realization that there wasn't going to be any change, so we decided, let's get with it and work it out," Deaver said.

Nowadays, the official view is that happy days are here again. "I'm happy," said Baker, who some intimates say is largely frustrated in his job.

Meese, not known for public pessimism, said: "In my opinion the system is working very well and the personal relationship among the four of us I think is extremely effective and the degree of communication among the four of us is extremely effective and I think is serving the president well."

Although they have come together in recent days to convince Reagan of the peril of failing to act to reduce burgeoning budget deficits, Reagan's top aides have not always been anxious to bring the optimistic president news he might not want to hear. Last year, for example, they often relied on Sen. Pete V. Domenici (R-N.M.) to be the bearer of bad tidings about the budget.

But there are two outsiders who often give Reagan frank assessments of his problems: California political consultant Stu Spencer, who recently spent two hours with Reagan over the holidays in Palm Springs, Calif., and long-time Reagan loyalist Lyn Nofziger, who still has direct access to the Oval Office.

Cabinet secretary Craig L. Fuller also has significant influence in the White House. He ostensibly reports to Meese but in fact plays a bridging role and has from the outset of the administration been the Meese person closest to Baker's staff.

There are several other presidential assistants who play intermittently important roles, among them communications director Gergen, spokesman Larry Speakes, intergovernmental affairs adviser Richard S. Williamson, counsel Fred F. Fielding, and political adviser Ed Rollins.

On any given day, a number of these officials may be in and out of the Oval Office. But they almost always are there on scheduled official business and accompanied by one or more members of the senior quartet.

Some officials, particularly those who have been associated with other presidents, observed that Reagan rarely engages in lengthy, informal exchanges when some immediate business is not at hand. "I've never been invited in to just kick off my shoes and talk," said one of them.

"I don't find the president sitting there getting good input on what's really happening today," said one official who is concerned about drift in economic policy. "He is probably the most detached president that has served in that office in a long, long time."