A revived lawsuit in Hennepin County claims that Medtronic shareholders collectively lost billions of dollars in investments when the Minnesota medical-device maker moved its headquarters to Ireland in 2015, and they are suing to get the money back.

The class-action plaintiffs scored a legal victory this week in their long-running fight against the world’s largest med-tech company, when Hennepin County District Judge Frank J. Magill declined to dismiss six of the nine claims in their lawsuit. The same court dismissed a similar version of the lawsuit three years ago, but the Minnesota Supreme Court reinstated it last fall.

The lawsuit says thousands of noninstitutional shareholders collectively paid as much as $3.4 billion in capital-gains taxes when Fridley-based Medtronic Inc. canceled its U.S. stock and issued shares of a new Irish company called Medtronic PLC in January 2015. The lawsuit also says shareholders lost as much $13.4 billion when their ownership was diluted through the acquisition of Covidien, which triggered the move to Ireland.

Plaintiff’s attorney Vernon Vander Weide in Minneapolis said Friday that the lawsuit is aiming to recover financial damages from the company, since it’s too late to unwind the merger of Medtronic and Covidien. The total damages for all claims could exceed $16 billion, the lawsuit says.

Medtronic spokesman Fernando Vivanco said Magill’s ruling is based on “preliminary legal issues” and doesn’t necessarily mean the shareholders will prevail.

“We intend to vigorously defend against the plaintiffs’ surviving claims, which we believe are meritless and should ultimately be dismissed,” Vivanco said in an e-mail. “Medtronic’s acquisition of Covidien was undertaken for strategic reasons, has created a company that has provided value for shareholders, and is positively impacting the lives of more patients, in more ways and in more places around the world.”

In January 2015, Medtronic paid roughly $50 billion to acquire medical supplier Covidien and move the combined company into Covidien’s former corporate headquarters on Lower Hatch Street in Dublin. Medtronic’s annual sales grew from $17 billion in fiscal 2014 to $28 billion in fiscal 2016. The price of Medtronic shares has risen about 25 percent since the deal. The stock closed at $96.41 on Friday, near its all-time high.

Although the deal may have turned out well for Medtronic as a company, the plaintiffs argue that Medtronic executives knowingly structured it in a way that harmed longtime individual shareholders — especially company retirees, who faced steep capital gains on small portfolios because their shares rose appreciably over decades. Some of them had to sell or donate part of their portfolio to cover the taxes on the remaining amount.

In their lawsuit, the shareholders say Medtronic diluted their shares by 30 percent and then forced them to pay capital gains taxes, even though some Medtronic executives knew that buying Covidien but keeping the world headquarters in Minnesota would have been less harmful financially for many shareholders.

The dilution happened because executives opted to structure the deal so that Covidien shareholders wound up owning 30 percent of the combined company. Citing internal documents obtained through legal discovery, the lawsuit says Covidien’s sizable share of the combined company was a strategic decision designed to protect Medtronic’s tax benefits by moving to Ireland.

The lawsuit also says Medtronic covered the cost of special taxes for executives to ensure that they voted in favor of the company’s interests and against the shareholder’s interests. The plaintiffs accuse Medtronic of withholding information that would have let shareholders cast better-educated votes on the deal.

Medtronic has argued repeatedly in court filings that the shareholders don’t have the right to file such a lawsuit, because Minnesota law typically gives corporate boards the right to determine whether a company’s actions harmed shareholders.

That argument convinced the Hennepin County court in March 2015 to throw out the first version of the shareholder lawsuit. But the Minnesota Supreme Court ruled last year that a deal such as Medtronic’s, known as a corporate “inversion,” can produce competing outcomes for the company and shareholders, which gives shareholders the right to sue.

Magill did throw out three of the nine claims in the revived lawsuit. The claims that were dismissed accused Medtronic and company officials of unjust enrichment, conspiracy to aid and abet unjust enrichment, and conversion.

The surviving lawsuit includes about two dozen plaintiffs today, including several Medtronic retirees. One of the next steps in the litigation will be for Magill to decide whether to certify the case as a class action.