Consulting giant McKinsey allegedly fed the opioid crisis. Now an affiliate may profit from treating addicts.

McKinsey & Co., the global consulting giant, agreed to pay nearly $600 million last week to settle allegations by 49 states that its work for large opioid manufacturers helped "turbocharge" sales of the drugs, contributing to an addiction epidemic that rocked the country and has caused more than 400,000 deaths.

The settlement is a black eye for the firm, which holds itself out as the preeminent global consultant advising corporations and governments. But because most of the money to be paid by McKinsey will go to state programs funding addiction...