The Supreme Court seemed to be looking for middle ground Wednesday while considering what has been called the biggest business case of the year: a battle between shareholders and corporations over securities-fraud class-action suits.

The corporations want the court to junk a 1988 precedent that has been a crucial factor in a series of suits in which investors have jointly sued over corporate statements they say misstate the health of companies and inflate their stock prices. Settlements in such cases have reached upwards of $70 billion.

After an hour of arguments Wednesday, it did not seem apparent that there were five justices willing to get rid of the “fraud on the market” presumption the court adopted in Basic v. Levinson. But it also seemed unlikely Wednesday that the court would be satisfied with the status quo.

The “fraud on the market” theory presumes that false statements by a company can improperly inflate the market price for its shares, so investors who buy stock at that price are overpaying and thus can later claim they were defrauded. According to this thinking, investors who claim they were defrauded do not have to show that they personally relied on the misstatements — or were even aware of them — in buying the stock.

Corporations claim the 1988 decision stacks the deck in favor of plaintiffs and forces companies into huge settlements. Four of the court’s conservatives have questioned the decision and called for a case in which they could revisit it.

Justice Anthony M. Kennedy, likely to be in the majority on a split court no matter how the case is decided, suggested that the court could leave the “fraud on the market” presumption in place but add a requirement — making investors show before a class action is certified that the stock was actually affected by whatever false statements are alleged.

“I call it the midway position,” Kennedy said.

The case before the court involves a group of shareholders, called the Erica P. John Fund, that is suing Halliburton. The fund seeks to represent all purchasers of the company’s stock between 1999 and 2001. They contend that the company lowballed its potential liabilities involving asbestos, inflated the potential benefits of a merger and misstated earnings reports.

The Supreme Court rejected Halliburton’s attempt to have the suit thrown out on other grounds in 2011, and lower courts certified the class and allowed the case to go forward.

The “fraud on the market” presumption is essential to such suits because it helps investors meet two class-action requirements: that they show they relied on a company’s false statements and that they share a common harm.

Houston lawyer Aaron M. Streett said Basic “was wrong when it was decided and it is even more clearly erroneous today.” He said the decision “substituted ­economic theory for the bedrock ­common-law requirement” intended by Congress, which is that shareholders must show they actually relied on the misrepresentations.

He faced tough questioning from the court’s liberals.

Justice Elena Kagan said Streett was wrong about congressional intent. “Congress has had every opportunity, and has declined every opportunity, to change Basic itself,” she said.

Kagan contested Streett’s position that the decision made class certification inevitable. “What we allow plaintiffs to do is to try to establish a presumption, which they do by showing that a particular market is efficient, and then we allow defendants to rebut that presumption,” she said.

But Streett said it was “virtually impossible” for companies to win that fight.

Justice Antonin Scalia, who along with Kennedy and Justices Samuel A. Alito Jr. and Clarence Thomas had expressed interest in revisiting the Basic decision, said Congress’s silence on the decision should be seen not as ratification but simply as an acknowledgment of the court’s action.

Chief Justice John G. Roberts Jr. questioned Streett’s argument that developments have undermined the economic theory behind the Basic decision. It is more of a matter of debate between the two sides, he said.

“How am I supposed to review the economic literature and decide which of you is correct?” asked Roberts, who is likely to be key to the outcome.

Kennedy repeatedly asked both sides if a compromise might be to require a study during the class certification process that would show whether the stock price was affected at the time by the false statements.

Streett said that would be his fall-back position. David Boies, representing the fund, was more resistent. “That’s very complicated,” he said. “It takes a lot of time. It’s very expensive. It’s a lot of expert testimony.”

In the case, the federal government is supporting the investors, and Deputy Solicitor General Malcolm L. Stewart was more receptive to the idea.

Getting rid of the “fraud on the market” presumption would have dramatic effects on class-action securities-fraud suits, he said. If the court adopted what Kennedy was suggesting, “I don’t think that the consequences would be nearly so dramatic,” Stewart said.

The case is Halliburton v. Erica P. John Fund.