New civil suits from the attorneys general in New York, Vermont and Washington State accuse distributors of brazenly devising systems to evade regulators. They allege that the companies warned many pharmacies at risk of being reported to the Drug Enforcement Administration, helped others to increase and circumvent limits on how many opioids they were allowed to buy, and often gave advance notice on the rare occasions they performed audits.

Three-fourths of prescriptions at a Queens pharmacy supplied by Amerisource were written by doctors who were later indicted or convicted, the New York complaint said. For more than five years, Cardinal shipped to a pharmacy with the highest oxycodone volume in Suffolk County, N.Y., despite continually flagging its orders as suspicious. McKesson kept shipping to two pharmacies six years after learning that they had been filling prescriptions from doctors who were likely engaging in crimes. The shipments stopped only last year, after the doctors were indicted.

“How do the C.E.O.s of these companies sleep at night?” Bob Ferguson, Washington’s attorney general, said at a recent news conference.