He who has no position in life cannot even get a dog to bark at him.

-- Niccolo Machiavelli

ROME, May 1 -- When Nancy Reagan flies here from Bonn Thursday for a two-day visit, protocol dictates that she stay with U.S. Ambassador to Italy Maxwell M. Rabb and his wife Ruth at the historic 17th-century Villa Taverna.

Though it is the U.S. ambassador to the Holy See, William A. Wilson, who will accompany Mrs. Reagan to a private audience with the pope on Saturday, and though Wilson and his wife Betty are among the Reagans' closest friends, the first lady cannot be their house guest. "Italians would be offended if she stayed at the Embassy Vatican," says a former American diplomat.

And as if the tug of war between those two ambassadors wasn't enough, there's a third who is very much a part of the American diplomatic scene here. Former New Jersey congresswoman Millicent Fenwick, however, keeps a much lower diplomatic profile -- at least among her countrymen, if not among her friends and the Romans -- in her role as U.S. ambassador to the U.N. Food and Agriculture Organization. She is not identified as an official participant in Mrs. Reagan's visit, according to information released by the U.S. Embassy.

This is one of a handful of places in the world with three accredited American ambassadors. And that makes for some tensions.

Diplomatic sources say it is not uncommon for Vatican ambassadors and their counterparts to Italy to feel a certain rivalry and "barely speak." The reasons can be as petty as worrying about how one's style of entertaining will stack up against one's colleague's.

While Fenwick goes her independent way, Rabb and Wilson are inevitably compared. As Reagan pals, the Wilsons are socially secure wherever they go. Elizabeth Wilson personally oversaw arrangements for the inaugural night party Saudi Arabia's Prince Bandar bin Sultan gave for the Reagans' California friends at his McLean home.

An Italian source says the Wilsons have "penetrated" Italian society, which the Rabbs apparently have not -- at least not beyond the Italian fashion crowd.

Millicent Fenwick, who can barely squeeze four people into the tiny library of her Rome apartment, almost never sees the Wilsons socially and remains aloof from internecine squabbling. She is frequently invited to receptions and dinners by the Rabbs, who often entertain her former congressional colleagues on Rome pilgrimages.

Diplomats of ambassadorial rank who have colleagues of equal rank posted here by their countries say it's an unwritten law never to invade each other's social domains. At least once, however, the Rabbs and Wilsons put forward a united front by cohosting a party honoring Gregory Peck, whose television film, "The Scarlet and the Black," was being previewed here.

Otherwise, the Wilsons entertain the Vatican clergy and the Rabbs entertain Italian government officials.

Rabb, who like Wilson declined to be interviewed this week, was known to be unhappy over the abundance of ambassadors. Though she had no comment on that, Fenwick says, "It's always difficult to have other ambassadors floating around." But, she adds, "As long as everybody sticks to their knitting there won't be any trouble."

Millicent Fenwick does not take the concept of turf lightly. And that may be the key to her compatibility with Rabb, America's senior diplomat here.

Consider his position: Within a year of Fenwick's appointment in the summer of 1983, Rabb found himself not the American ambassador here but one of three. The Fenwick appointment came two years after his and was quickly followed by Wilson's rise from U.S. representative to the Holy See in February 1981 to the rank of ambassador in March 1984.

Sources say that Rabb, who likes to joke that he speaks "fair to middlin' " Italian, reportedly was furious at first over her appointment. "She gives interviews in Italian, and that just underlined Rabb's inadequacies," said a former diplomat.

And on the subject of the need for the Vatican Embassy, Rabb told a dinner companion at the State Department in March, "Don't get me going on that one."

Some months after Fenwick arrived, she said she began to realize that a member of her mission was bypassing the Embassy Rome (as the American Embassy is known in order to differentiate it from the Embassy Vatican) to talk directly to the Italian deputy minister of foreign affairs. She asked Rabb if it would be "inconvenient" for him to send along his political officer when meetings were arranged. He did.

Rabb also includes her in his Friday morning "country team meeting," though Wilson is not invited. "It's probably a courtesy thing," Fenwick acknowledged, "but we get along very well, and I admire him very much."

The American ambassador's official residence is a 17-room mansion hidden behind a 14-foot-high wall. Villa Taverna is a showcase of American art and period furnishings, some of which were provided by tax-deductible funds raised through the Villa Taverna Foundation.

Embassy Rome refused to comment on all aspects of Mrs. Reagan's visit, so it is not known which bedroom she will occupy. It was in a second-floor bedroom at Villa Taverna that arsenic particles fell from the painted ceiling, contaminated the morning coffee of then-ambassador Clare Boothe Luce and resulted in the headlines that she had been poisoned.

Some credit Rabb's success with Italian politicians as the result of understanding "Machiavellian politics." And they give him high marks for his efforts in trade as well as security; when Gen. James Dozier was kidnaped in December 1981, Rabb showed American security officers that they were not going to run the show.

Fenwick tells of sitting next to President Sandro Pertini at a lunch across the table from Rabb. "Pertini turned to me and said, 'I love that man.' And I think the reason why is that Max Rabb does not feel you tell allies, you consult them."

The Wilsons live in a rented 19th-century residence called Villa Richardson. It also sits behind high walls, on the Janiculum, one of the hills on which Rome is built. Small by embassy standards, the house has four bedrooms and a large dining room. Friends say Betty Wilson's use of pastel chintz and white carpeting, punctuated by some Italian antiques, was the work of First Decorator Ted Graber, although she told Architectural Digest in November 1983 that she had decorated it without professional help. "It's small but it's enchantingly California-like," says a New York friend.

Wilson, a Roman Catholic convert, has not simply the political support but personal friendship of Ronald Reagan. But his foreign colleagues say he is often traveling and that he is not a frequenter of their diplomatic circuit. And he is seen by some Americans here as, at the very least, politically naive.

There is one constant in Vatican ambassadorial entertaining: The pope never comes to dinner. Neither does he invite ambassadors to dine with him. The rest of the Vatican hierarchy, however, is eager for home-cooked meals. "It's hard to balance the table," says a hostess. "On the other hand, conversation is very stimulating because you have some of the best minds in the world sitting at your table. Still, you have to love Rome, have an interest in art history and religious affairs. There's nothing like the Kennedy Center here."