State attorneys general investigating Alphabet Inc.’s Google may seek a break-up of its digital advertising operations if they sue the internet giant over antitrust violations, according to people familiar with the probe.

A break-up, which can only be imposed by a court, is among a range of options the states are considering as part of a lawsuit against Google.

The states are gathering evidence for their case, which was opened last year and isn’t yet in final stages, said four people familiar with the discussions who asked not to be identified discussing a law-enforcement matter. Decisions on remedies generally aren’t made until much later in the process and after a lawsuit is filed.

While break-up proposals have faced uphill battles in court, the attorneys general want to take strong action against the search engine and are concerned that billions in fines levied by the European Union have failed to stop what they see as anticompetitive conduct. One of the people said that Google rivals working with the state enforcers have largely spoken under formal demands, which means that their statements can be introduced as evidence at trial.

As the states build their case, the Justice Department is also drafting a complaint against the company.

The digital advertising market is the main focus of Texas Attorney General Ken Paxton, who is leading the 48 state law enforcers looking into the company, although other states within the group are also scrutinizing its role in the online search and mobile operating system markets.

“The facts are clear: Our digital advertising products compete across a crowded industry with hundreds of rivals and technologies, and have helped lower costs for advertisers and consumers,” a Google spokeswoman said.

A break-up of Google’s ad tech business won’t be enough on its own to remedy the company’s anticompetitive conduct, said Gene Kimmelman, a senior advisor at Public Knowledge, a Washington-based policy organization that recently published a paper outlining how enforcers could build an antitrust case against Google.

Even with a sale of some Google ad businesses, the company could rebuild its dominance in the market by putting restrictions on advertisers and publishers that force them to go through Google still, Kimmelman said.

“It’s a matter of combining whatever assets appropriately might need to be split off, while preventing Google from bundling and tying arrangements with their other dominant services,” he added.

In the last major monopoly case brought by the U.S. — the 1998 lawsuit against Microsoft Corp. — a judge initially ordered the break-up of the software company. That decision was overturned on appeal in 2001 and the George W. Bush administration settled the matter in 2002, with Microsoft agreeing to court supervision for many years.

U.S. federal and state authorities are asking detailed questions about how to limit Google’s power in the online search market, Bloomberg reported Thursday, citing rival DuckDuckGo Inc.

Last year in Europe, Google was fined 1.5 billion euros for thwarting advertising rivals, the year after it faced a record 4.3 billion euros for antitrust violations over its Android mobile operating system. The year before that, it suffered a then-record 2.4 billion euro fine following an investigation into its shopping-search service.

Last year, Google’s online search ad business generated almost $100 billion in revenue.

The Federal Trade Commission, which also enforces U.S. competition law, previously investigated whether Google stifled competition in the market for online search advertising, but it closed the probe in 2013 after the company agreed to relatively minor changes.

The consideration of a break-up of Google’s digital ad business by state attorneys general was reported earlier by CNBC.