Next on Reagan agenda: shakeup at White House?

President Reagan has moved into a new phase of his presidency. Major staffing changes, if not a White House restructuring, may be needed, political scholars here say.

Beleaguered when only weeks ago he was applauded, Mr. Reagan finds his key domestic and foreign-policy aides under fire. He sees the allied community worried over US saber-rattling and a sharp cleavage growing between economic classes at home over his policies. And he hears forecasts that his party will succumb to the historical pattern of losing seats in the fast-coming 1982 elections.

The President is taking some stopgap measures. His Nov. 18 foreign-policy address was hastily pressed forward to stem fears about America's nuclear-weapons plans in Western Europe, and to put him before the public at a time when his staff and policies appear in disarray. Political observers note that Mr. Reagan's personal popularity is his chief asset at the moment, but they wonder how long it can continue to carry his administration.

''The administration has settled down into the normal pattern of being beleaguered,'' says historian Frank Freidel, formerly of Harvard University and now at the University of Washington in Seattle. ''If you were to go back to the Franklin D. Roosevelt administration, by the end of a year the attacks were coming.''

''How Reagan handles these things - whether they are quickly forgotten or whether they go on and on and he has to cut his losses - is more important than the events themselves,'' Mr. Freidel says.

FDR also had to deal with a case like David Stockman's, the Reagan budget director under fire for comments on the President's economic program. FDR's brilliant policy architect, Raymond Moley, was attacked in the press for his behavior at the London economic conference at the end of FDR's famous first 100 days. FDR quietly eased Mr. Moley out of Washington. And Freidel recalls the furor that beset ''good, gray Dwight D. Eisenhower over Sherman Adams and a vicuna coat.''

Quick action is needed by Reagan to avoid what happened to President Carter during the case of his budget director, Bert Lance. ''A vast amount of the clout of the administration evaporated during the long time the Lance case was in the forefront of people's thinking,'' Freidel says.

Reagan's problems at the moment are only partly personnel. The time is about right for some reshuffling of Cabinet posts, says Stephen Hess, Brookings Institution expert on White House staffing. ''It is a time for careful reevaluation of whether the right people with . . . the right chemistry with the President are now in the right job,'' Mr. Hess says.

''It should be a positive sign if, nearly a year into an administration, a president made some very substantial changes.''

''In the natural history of an administration, you bring in a lot of people who are strangers to each other,'' says Hess. ''You're expected to continually evaluate them and to make adjustments - just as you make fine tunings on the lower White House staff.''

Presidents pay a price by reshuffling under fire. ''It's going to be perceived as admitting mistakes,'' Hess says. ''But there are far worse things than admitting mistakes.''

White House changes could include both foreign and domestic posts. National security adviser Richard Allen, under fire for a $1,000 gratuity incident and for feuding with Secretary of State Alexander M. Haig Jr., is one of the more obvious targets.

Some Reaganites, however, think the crux of the President's problem may lie less in the personalities of his aides than in the structure of his operation. It may not be the Haig-Allen turf fight - seen as routine in Washington - but the awkwardness of trying to funnel foreign policy through the President's troika.

Presidential counselor Edwin Meese III, one of the troika, was heavily criticized early in the Reagan campaign for inadequately preparing the candidate. John Sears, Reagan's take-charge campaign manager, was eventually fired as Reagan tardily brought back his longtime aides. Secretary Haig, whose penchant for command impels him to a lead role, might well continue to feel balked at the White House, whatever happens to Allen. A stronger role for Vice-President George Bush in foreign policy would only increase the crowd at the decision point.

Cabinets and White House staffs are often initially put together to satisfy constituents. A year into office is not too early to reward by advancement those appointees who do well on the job, and to ease out others, Hess says.

Stockman, while credited with engineering early White House victories on Capitol Hill, may have finished his main work. Reagan's first major Capitol Hill defeat this week, on a budget funding issue, suggests an era of negotiation and compromise may now be needed.

''Even if it weren't for this (Stockman's public criticism of Reagan's economic program), never again would Stockman or anyone else be able to get Congress to act as rapidly as it did this last summer,'' Freidel says. ''That was the kind of phenomenon that comes only once in many, many years.''

Domestically, Reagan must now preside over a new, more technical stage, in which lobbies must be countered and adjustments made, Freidel says. In foreign policy, the demands are even more urgent, as the administration must yet find a way to think and speak with one voice.