Members of the Sackler family who own OxyContin maker Purdue Pharma, maker of OxyContin, are willing to kick in more money – up to $6bn in total – to settle thousands of lawsuits over the toll of opioids as the company tries to work out a deal with state attorneys general who torpedoed an earlier settlement. The offer was detailed in a report filed on Friday in US bankruptcy court by a federal mediator who asked the court to let her have until the end of the month to broker a new settlement. Under the latest proposal, the Sacklers would contribute between $5.5bn and $6bn, an increase from the $4.3bn they had agreed to in the original bankruptcy settlement. The last of the money would not be paid out for 18 years, and the exact amount would depend on how much the family would make from selling its international drug companies. The additional money would have to be used to combat a crisis that has been linked to more than 500,000 deaths in the US over the past two decades. Part of it would be controlled by the eight states, joined by the District of Columbia, that objected to the original settlement last year even when other states agreed. In exchange, members of the family would be shielded from current and future opioid-related lawsuits. That protection was contained in the original settlement but prompted the objecting states to file an appeal that ultimately succeeded, leading to the current negotiations. The objecting states said the earlier amount of $4.5bn did not go far enough to hold accountable members of a family that made billions from the sale of OxyContin. Advocates for opioid victims and their families were concerned about where the additional money would go. Ryan Hampton, an advocate for people with opioid use disorder, said it did not appear that the $750m set aside for payments to victims of the crisis and their families would increase under the latest proposal. “The government’s pot will continue to get larger as additional settlement negotiations may continue, yet there’s no increase for direct payments to families and survivors,” Hampton said. “It’s dead wrong and unjust.” According to the report by the mediator, the US bankruptcy court judge Shelley Chapman, any new deal would be contingent on having all the holdout states and the District of Columbia agree to it. She said a “supermajority” have agreed so far, but did not list which are still holding out. Offices of state attorneys general declined comment or did not respond. A spokeswoman for one branch of the Sackler family also declined to comment, while a representative for the other side did not respond. In a statement, Purdue said it remained “focused on achieving our goal of providing urgently needed funds to the American people for opioid crisis abatement”. This week, the US bankruptcy court judge Robert Drain agreed to keep any opioid lawsuits against Purdue and the Sacklers on hold through 3 March, to buy more time for reaching a settlement.