Can Ronald Reagan find four two-headed Cabinet officers? That question poses, metaphorically, the fundamental problem raised by the president-elect's approach to the building of a new administration.

So far nobody knows the answer. For what Reagan has in mind is something new and untried -- an interesting experiment.

Government by executive committee of the Cabinet is the name of the experiment. The basic idea is: four leading Cabinet officers -- the attorney general and the secretaries of state, defense and Treasury -- form a committee of top presidential advisers. They will work initimately with the president in framing a general policy for the next four years and in making all major decisions.

The White House staff would be shaped to serve the Cabinet committee. It would be trimmed and disciplined so that no individual members could go into business themselves. Instead of striving to impose the president's will, the staff would help the president and his advisers work with Congress and the rest of the government.

A critical step in putting this support structure in place came with the announcement of two White House staff members last week. Edwin Meese, who served as Reagan's chief of staff in Sacramento and during the campaign, will be a presidential counselor linking the White House staff to the Cabinet committee. He will have Cabinet status and supervision over the two major White House policy organs -- the National Security Council staff and the domestic policy staff. James Baker, who managed President Ford's campaign in 1976 and the campaign of George Bush this year, will serve under Meese as White House chief of staff. He will supervise the more mandane, day-t0-day business, including relations with the press and Congress.

Two persons better qualified for senior managerial posts are hard to imagine. Meese and Baker have the confidence of the president-elect. Both care about making things work. Both are well equipped to keep self-promoters from fighting battles the president doesn't need against enemies he does not have.

Still there are questions. How can Meese, who has little foreign policy experience, effectively oversee the NSC staff? How can Baker control relations with the media? More important, how do they prevent outsiders from playing one off against the other in ways that build into the White House a power conflict?

Filling the front-four Cabinet positions presents even greater difficulties, for it is no exaggeration to say that the right people need two heads: one head to answer the needs of the demanding departments with strong priorities and special interests, another head to assume the president's perspective and take into account everybody's business.

The new secretary of state must have the intellectual grasp and moral authority necessary to balance foreign against domestic claims in a way that is convincing to the American people and Congress. A big part of the job also involves exacting sacrifice from the allies and being firm with the Russians without exciting the paranoia to which both parties are now prone. In the bargain, the secretary will have to keep top-dog status with the president, which means not exciting the suspicions or the envy of the Pentagon.

The new secretary of defense needs the moral stature required to make the armed forces swallow something less than everything. Guns have to be balanced against butter (or rather, inflation). The security advantages that spring from an arms control arrangement with Moscow have to be pushed past the military and a Congress and public prone to jingoism.

The new secretary of the Treasury must command the respect that makes it easy for other leading economic officials to subordinate themselves. Another essential is the respect of the congressional leaders, who, after all, write the tax laws. Then there is wanted the automatic confidence of the business community -- that is to say, a confidence not gained by spouting silly slogans about free enterprise.

The new attorney general has to run a department stuffed with self-starting prosecutors who tend to regard any president as Public Enemy No. 1, and his associates as partners in crime. Outwardly plausible, but inwardly ill-founded, cases have to be turned off without courting public suspicion. In addition, single-interest groups bent on junking up the congressional, and even the constitutional, agenda with retrograde measures will have to be gently turned off. Persons to fill those exacting requirements do not come easily to mind. But nothing less will do at a time of American decline in both economic strength and international stature. So, while I wish the new administration well, I find it hard to share the flush of exuberant optimism that has suddenly suffused the capital.