SAN FRANCISCO — Theranos Inc. seems to be slowly digging out from the pile of litigation that threatened to bury the company last year in the wake of damning reports about its technology.

On Tuesday, a federal judge in Arizona swept away most of the dozen-plus class action claims against the once-vaunted blood testing startup and former pharmacy partner Walgreens, brought on behalf of patients in that state and California who took Theranos tests.

U.S. District Judge Russel Holland definitively rejected conspiracy and medical battery claims advanced by lawyers for the proposed class at Keller Rohrback and Lieff Cabraser Heimann & Bernstein. But Holland allowed parts of their fraud and unjust enrichment claims to advance, giving the plaintiffs another chance to fix some deficiencies he found in their pleading.

The judge seemed skeptical of defenses by Theranos and Walgreens that they are shielded from certain fraud claims relating to advertisements about the blood tests. The companies argued they were nothing more “puffery” and thus allowable under the law.

But Holland wrote that statements like “we continuously conduct proficiency testing and participate in multiple proficiency testing programs” are not puffery. “As for defendants’ alleged misrepresentations about Theranos testing being accurate and reliable, it is at least plausible that these statements may not be puffery,” the judge added.

After The Wall Street Journal published a series of exposés calling into question Theranos’ testing technology, the company was forced by regulators to curtail its operations and void or issue corrected blood test results.

A wave of false advertising class actions was filed in both Northern California, where the company is headquartered, and in Arizona where Theranos had operations and offered its blood tests through Walgreens. They were eventually consolidated in Holland’s courtroom.

Michael Mugmon, a partner at Wilmer Cutler Hale Pickering & Dorr in Palo Alto who represents Theranos in the litigation, on Wednesday expressed satisfaction at the judge’s ruling. “Theranos is pleased that the result takes us one step closer to putting this litigation behind us,” he said.

A spokesman for Walgreens, represented by Weil, Gotshal & Manges partner Diane Sullivan, declined to comment. Lynn Sarko, a partner at Keller Rohrback in Seattle and one of the lead lawyers for the proposed class, could not be immediately reached Wednesday.

Theranos in April announced a $4.46 million settlement with the Arizona attorney general to refund customers who bought its tests, and in May announced it had settled suits brought by two of its early investors. But it still faces a class action brought on behalf of indirect investors pending in the U.S. District Court for the Northern District of California, and a breach of contract suit brought by Walgreens.