THERE ARE three ways to do away with extra-billing for medical care: ban it, make it so unattractive doctors won't bother, or pay doctors enough to keep them happy without it. Ontario's minority Liberal government, trying to avoid an all- out war with the province's 15,000 physicians, seems ready to try all three.

Legislation to ban extra-billing - charging for medical services in excess of provincial health plan rates - should pass second reading in the Ontario legislature this week. From there it heads to committee, where amendments seeking to resolve the bitter dispute may be put forward.

It is scarcely surprising that Ontario should be the major battleground in the Ottawa-led campaign against extra-billing. The province's doctors have a history of militancy, and the practice is more deeply rooted there than in any other province.

''The main extra-billing question in Canada is in Ontario,'' says federal Health Minister Jake Epp.

It is, nevertheless, something of a twilight struggle. After Ontario, extra-billing remains a fact only in Alberta and (less so) New Brunswick (see box). Ontario's bill, if passed, would make the province the fourth to legislate against extra- billing since passage of the federal Canada Health Act in 1984, in the last year of the Liberal ancien regime.

Under the act, which Epp's Conservatives supported in opposition, the federal government withholds from a province one dollar in Established Programs Financing for every dollar extra-billed. (The money is refunded if the province passes legislation against extra-billing before June 30, 1987.)

Two provinces - Nova Scotia and Manitoba - have banned the practice, and have instituted arbitration procedures for settling fee disputes.

Saskatchewan, following the model established in Quebec in 1970, allows doctors to extra-bill, but forces them to withdraw from the provincial health plan and recover the full amount of the fee from the patient - an elegant solution which quickly eliminates the practice.

Ontario's Health Care Accessibility Act follows the Nova Scotia-Manitoba model. Doctors may still opt out of the Ontario Health Insurance Plan, but neither they nor ''opted-in'' physicians may charge in excess of OHIP rates. Those who do face fines of up to $10,000.

Sinking into the rich loam of rhetoric the controversy has produced, it is not difficult to imagine the Russians have landed.

''This is the worst law in Canada. It's worse than anywhere in the world - even behind the Iron Curtain,'' says Dr. Earl Myers, president of the Ontario Medical Association.

''It's communistic,'' splutters Dr. Howard Eisenberg, chairman of the Association of Independent Physicians, an OMA sub-group representing the doctors most directly affected by the ban. ''They're enslaving the physicians.''

On the other side, lurid stories appear in the press of patients in hardship because of extra-billing. The Toronto Star found a 70-year-old one-eyed diabetic forced to go without grocery money to pay for operations, who would not have her name printed for fear of reprisals from her specialists.

In fact, the practice, even in Ontario, is relatively rare. Nine out of 10 Ontario doctors charge OHIP rates, and receive payments directly from the Plan. ''Opted- out'' physicians negotiate fees with patients, who are reimbursed by the province to the level of the corresponding OHIP rate and pay the difference themselves.

About 6% of services in Ontario are extra-billed, concentrated among specialists (who are in short supply) and in the affluent Toronto area. Billings in excess of OHIP amount to just 2% of the $2.2 billion in total fees. And doctors argue that poor patients are rarely extra-billed.

Each side in the dispute insists it is prepared to compromise. Yet each maintains its base position - for or against extra-billing - is non-negotiable.

The physicians say they are willing to discuss extra-billing in the context of an overall health review, and to ensure that no hardship cases are extra-billed in the meantime. The hope is that the review would provide sufficient cover for the ban to be quietly buried.

The government, for its part, has suggested it might phase in the ban, reduce the fines, introduce ''merit pay'' and fee arbitration, or substitute the Quebec model. But, whatever its form, the ban stays.

So, with scant prospect for agreement, the OMA girds for war. Says Dr. William Vail, a Newmarket, Ont., MD who also happens to be president of the Canadian Medical Association, ''If we go down, we're going to go down with a fight.''

Tactics endorsed by the OMA's 250-member council: - Mass opting out of physicians from OHIP, aimed at jamming the system with paperwork. - A work-to-rule ''Health Care Awareness Week,'' date undetermined. - A ''civil disobedience'' campaign, in which doctors will break the law by extra- billing token amounts. - On the other side of the law, a court challenge on Charter of Rights grounds. The CMA already has legal action against the federal bill before the courts, arguing it encroaches on provincial jurisdiction.

But the Ontario doctors, in tough against a still-honeymooning Liberal government (54% in the latest public approval pulse-taking), stopped short of the rotating walkouts used to good effect in a 1982 fee dispute with the former Conservative government.

Such a tactic might offer the government a convenient excuse to call an election, which on present form it would win handily. What the doctors need is a dispute of sufficient length and rancor to produce the kind of generalized public disaffection which often attaches itself to the government of the day.

Whatever the politics of the issue, more heat than light has been shed on its substance. Evidence on the extent to which access to health care actually is constrained, for example, is scarce, ranging from the anecdotal to survey data of arguable significance.

Often quoted is a 1980 study by Professors Greg Stoddart and Christel Woodward of Hamilton's McMaster University. In a survey of 1,769 households in four Ontario counties with heavy incidence of extra-billing, they found that 28% of poor families said doctors' fees created financial problems for them. Less than 5% of those surveyed found this sufficient inducement to try another doctor, however; only 3.5% even asked for a lower fee.

Another study, released late last month as the Ontario Coalition of Senior Citizens Organizations waded into the fray, said 62% of senior citizens have been extra-billed. The implication of this would appear to be either that doctors lie in wait for senior citizens, or that the elderly carefully seek out the most expensive physicians.

Ontario Health Minister Murray Elston is convinced accessibility is threatened. He tells of a man in his constituency who was charged $400 extra for an eye operation.

''It was only at the time that this thing was finally scheduled...that he's told that he's going to have an extra-billing problem. He has no money, he's on welfare because he's not working because of his eyes,'' Elston says. ''It may be anecdotal to you but it sounds pretty bad to me.''

Dr. Michael Rachlis, spokesman for the Medical Reform Group, a small but high-profile association of doctors which supports the ban, says accessibility can be denied in subtler ways. A physician, for example, may refer patients who cannot afford extra charges to hospital outpatient clinics, rather than treat them personally.

Whether banning extra-billing for all is the solution to a problem affecting a few is a different question. Some doctors have suggested low-income patients should carry identification cards exempting them from extra-billing, much like the cards senior citizens use for discounts on other services. Elston dismisses this with some contempt as ''charity medicine.'' Universality rears its sacred head once more.

The government also argues the bill is necessary to recover withheld federal funds. The amount involved, however, an estimated $53 million in 1985, is a drop in the bedpan compared to the province's $8.9-billion health care budget.

The doctors, meanwhile, emphasize the threat to their ''independence'' posed by the ban. They say it will mean further state control of the medical profession; indeed, to hear the OMA's Myers quoting Rev. Martin Niemoller (''Then, they came for the Catholics....''), of society in general.

Without the ''safety valve'' of extra-billing, they argue, they would be less free to act as independent health care critics. They would also, of course, have less leverage in fee negotiations with the government, though this is rarely mentioned: the OMA is careful to downplay the issue of doctors' incomes.

As well they might. Doctors have long been the most richly rewarded of the professions. In 1983, the latest available year for Revenue Canada taxation statistics, self-employed doctors reported average income after expenses of $89,124 - more than five times the average for taxpayers in general.

That puts them well ahead of dentists ($76,690), lawyers ($61,457), accountants ($51,412) and engineers and architects ($45,119). State medicine has not been entirely disagreeable to the profession.

Hence, perhaps, the absence of any rush for the exits. Health & Welfare Canada has 418 doctors recorded as leaving the country in 1984 - about the same as in the 1960s, before medicare was introduced nationally, and less in proportion to the number of doctors in the country (about 44,000 now, compared to 25,000 then). More doctors, in fact, are entering the country than leaving.

Doctors' cries of laissez-faire, moreover, run the risk of appearing more than a little disingenuous, given that the profession is itself a closely hedged-about cartel; a reminder of which was provided last month in Ontario's legal recognition of midwifery - a bit of free enterprise competition the doctors had fiercely opposed. In this light, banning extra-billing amounts to regulating a monopoly.

Justice Emmett Hall, in the 1965 royal commission report which led to the establishment of state health insurance across Canada,says: ''when the state grants a monopoly to an exclusive group to render an indispensable service, it automatically becomes involved in whether those services are available and on what terms and conditions.''

Free market advocates might suggest a better way to deal with the problem: break apart the monopoly. That, however, would require more radical surgery: full-scale health care reform. For that, breathe deeply - and wait.

WHERE THE PROVINCES STAND

BRITISH COLUMBIA

Extra-billing within provincial medical plan banned in 1981. Doctors may still opt out and extra-bill as in Ontario; few do. Doctors' earnings historically among highest in country.

ALBERTA

Extra-billing allowed even within plan, although incidence ebbing. Government disinclined to ban extra-billing, but keen to recover $11 million a year in funds withheld by Ottawa since 1984 Canada Health Act. Some talk of moving to current Ontario system.

SASKATCHEWAN

1985 law forces doctors wishing to charge above health plan rates to withdraw from plan, recover full fee from patient. Rider: access must not be jeopardized. Four Regina ophthalmologists who opted out were ordered back on plan (one later won right to stay out).

MANITOBA

Extra-billing banned in 1985; binding arbitration on fee disputes introduced.

ONTARIO

Doctors currently allowed to extra-bill outside of plan; patients are reimbursed to health plan rates, pay difference. December, 1985 legislation would make extra-billing in or out of plan illegal.

QUEBEC

As part of 1970 medicare bill, doctors must withdraw from plan to extra-bill, patients not reimbursed. Few doctors are opted out.

NEW BRUNSWICK

Small amount of extra-billing ($85,000 annually).

PRINCE EDWARD ISLAND

No legislation, but agreement by doctors not to extra-bill.

NOVA SCOTIA

First province to pass law (1984) against extra-billing after federal legislation. Binding arbitration, as in Manitoba.

NEWFOUNDLAND

No ban, but extra-billing a non-issue. Spread between doctors' earnings and average taxpayer's is highest in country (a factor of seven).