The justices seemed by turns reluctant to break up an exhaustively negotiated agreement, but also leery of somehow rewarding the Sacklers.
The OxyContin manufacturer has long been accused of ignoring the drug's addictive qualities in favor of profit.
The family will receive full protection from civil legal claims under the deal, which was approved by a federal appeals court.
A federal judge has overturned a pharma settlement that left the Sackler family free from lawsuits over the opioid crisis.
The family has drawn ongoing furor over its role marketing OxyContin to Americans.
States agreed to sign on after the Sacklers kicked in more cash and accepted other terms, including apologizing.
The decision follows years of demonstrations against the museum's connections to the philanthropic family that profited off the opioid crisis.
The Sackler family will give up ownership of the company and contribute $4.5 billion but will be freed from any future lawsuits over opioids.
A U.S. bankruptcy judge is expected to rule on whether the OxyContin maker will settle thousands of lawsuits.
The owners of Purdue Pharma may soon be immune to future litigation over their role in the opioid epidemic under a bankruptcy plan advanced by a federal judge.