First lady Hillary Rodham Clinton has her eyes on the Senate. Vice President Gore has his on the Oval Office. And President Clinton's gaze is fixed on history.

Suddenly this spring, the Clinton White House has found itself home not to one ambitious agenda but to three. And aides say that is making it a very complicated place to work.

Three powerful personalities are striding across the political stage, each one supported by a coterie of advisers more loyal to their particular leader than to the trio as a whole. Crossed signals are becoming commonplace. So are the cross feelings that inevitably result.

The jostling personal agendas have involved political logistics, including conflicting fund-raising schedules, confusion over each other's news media appearances, and competition over who gets to make the announcement when the administration has news to announce. Gore, advisers said, sharply instructed his team last week to stop speculating about whether the first lady's likely Senate campaign in New York was good or bad for his presidential bid, because the speculation itself was becoming a hindrance.

Beyond politics, there is a substantive dimension to the phenomenon that a former Clinton aide called the "three-headed White House." White House economic aide Gene Sperling this month sounded an alarm when he feared that Gore's new education proposals might be at odds with Clinton's fiscal policy; some specifics were diluted at the last moment. In a meeting with New York hospital executives, according to published reports, Hillary Clinton left the impression that she had reservations about how the state was being treated under the administration's Medicare policy.

"It's uncharted territory," said one senior congressional staff member who works frequently with the White House. "They could become in substantive conflict, that's for sure."

More broadly, several administration officials last week acknowledged that the president is likely to be confronted repeatedly over the next year with a fundamental choice. He has said often he wants to make his last stretch in office a season of legislative achievement, striking bipartisan agreements on his free-trade agenda and repairing ailing entitlement programs such as Medicare and Social Security. Such accomplishments would count as impressive triumphs and would burnish Clinton's legacy.

But such victories would almost certainly involve compromises with Republicans that the first lady or the vice president might be loath to make. For instance, if compromises on trade issues such as letting China into the World Trade Organization alienate union activists, that would cause problems for candidates trying to keep a Democratic coalition intact. A centrist agreement on Medicare for instance might be seen as a lost opportunity for Gore and Hillary Clinton, if it removes the issue of protecting senior citizens from the election agenda.

"There's no doubt it's complicated," said one former administration official who remains close to many in the White House. "You've got two people trying to campaign, and one person trying to govern."

White House officials say they know there will soon be confronting efforts by reporters and Republicans to find policy differences among the president, vice president and Hillary Clinton. A move by the president to nudge Israel in the Middle East peace process, for example, might not necessarily go over well with many Jewish voters in New York.

"I can imagine [Republicans] dreaming up ways to draw attention to differences," said James Pfiffner, a George Mason University political scientist.

One administration official close to the political advisers of Gore and both Clintons invoked a sports metaphor: "There are three major league baseball teams on the field right now, and they're all trying to get the best players and make the best plays."

There is precedent for this elbowing within the Clinton White House. In 1993, Gore was battling bureaucratic waste with his "reinventing government," Hillary Clinton wanted the White House agenda kept clear for her health care proposal, and the president was insisting that sufficient lobbying and communications time be reserved for winning the North American Free Trade Agreement. But that fight was about the Clinton presidency. Now, Gore and Hillary Clinton are both trying to elevate their status and move beyond that presidency, in what one administration official called "a psychodrama in action."

If so, it is a drama in which the actors fundamentally wish each other well. Clinton, aides say, regards Gore's election as his successor as a top priority, and is encouraging of a Senate bid by the first lady. Moreover, the principals have tried to keep the White House from becoming a Medusan tangle. While only Gore is so far raising money for his own campaign, both Clintons have active schedules on behalf of Democratic groups. And when any one of the three holds an event in a city, it basically soaks up contributions for several weeks. After some bobbled events a few months ago, the president ordered deputy chief of staff Steven J. Ricchetti to coordinate fund-raising schedules.

And, while political professionals say the first lady's New York run is fraught with potential hazards (as well as some benefits) for Gore, aides said the vice president feels strongly that she is entitled to do whatever she wants, with no sniping from his side.

But this good will at the top masks a more complicated dynamic lower down in White House ranks. "There are resentments in all three directions," said one political operative close to both Clintons and Gore. "There needs to be much better coordination."

Take the question causing the most fevered speculation of any in political circles these days: What are the first lady's plans? One bad place to search for answers is the White House West Wing, where many of Clinton's senior advisers say they learn more from the newspapers and outside gossip than from official channels. For years, White House officials say, Hillary Clinton has been reserved toward most of her husband's top aides, and downright suspicious toward some of them.

"Hillaryland is Hillaryland," said one adviser to the first lady, using the White House's slang term for her tight inner circle. "I think the West Wing is always interested in what she's doing. I don't think she tells them anything."

The lines of communication are more open between Clinton's staff and Gore's. Increasingly, however, sources say these two operations have been viewing the other with mutual frustration and incomprehension.

Gore's staff, according to a variety of White House and outside sources, sometimes bridles at what aides consider the difficulty of getting certain administration policies reserved for Gore to announce and promote -- as well as the trifling nature of some of what does get handed off to the vice president.

Many on Clinton's team, meanwhile, say they are happy to help Gore -- and in fact are under instructions from the president to do so. But sources said senior members of Clinton's staff often feel unconsulted and underutilized by Gore's team. On several occasions in recent months, these sources said, Clinton's advisers were left shaking their heads in bewilderment at what seemed to them like clumsy political moves by Gore or his staff.

"From the Clinton folks' perspective, there's a sense of `Who's in charge?' and `How are we supposed to help if we don't know?' " said one White House policy aide. "From the Gore perspective, they feel they shouldn't have to be asking for things, we should be proactively giving them stuff."

A section of the budget last winter was essentially Gore's -- environmental proposals to improve "livability" of urban areas. But Gore aides brayed to the White House this month when a mental health initiative got leaked to the news media; they thought it might have made a good item for the vice president or Tipper Gore to announce.

Often what Gore gets is relative trivia, such as last month's release of Agriculture Department funds for rural rental housing subsidies. Gore advisers say such micro-announcements are of little value in trying to project presidential stature.

Increasingly, Gore is a much less overt presence at the White House -- as he is on the road more often, determined to be more of a candidate and less of an understudy. The same is true of the first lady. White House aides say she is so busy traveling that scheduling events where both Clintons are expected, such as a presidential medal of honor ceremony, is becoming difficult.

Both Hillary Clinton and Gore are stepping up media appearances. In most cases, aides say, they don't coordinate with White House communications staff as they would have in an earlier day. In some cases, they forget even to inform these people. After the Columbine High School shooting, White House aides learned shortly before air time that Gore was going on CNN's "Larry King Live" to talk about the tragedy.

White House aides say Clinton misses the more constant presence of Gore, particularly on difficult issues such as Kosovo, even though they share views by phone or through senior staff. "It's stupid to deny it," said one senior official. "You lose a beat when you're not in the room."

White House senior adviser Douglas B. Sosnik acknowledged that the administration confronts a unique challenge in coordinating three different ambitions, but predicted the task can go smoothly. "By any historical standard, it's fair to say there's more cooperation between the president and vice president and their staffs than any we've seen in recent times," he said. "That will serve us well in the next 18 months, and if Mrs. Clinton chooses to run for Senate, I would expect the coordination between all our offices to work smoothly as well."

CAPTION: President Clinton, Hillary Rodham Clinton and Vice President Gore have competing agendas as Gore and the first lady plot their political strategies.