You can always do not accept their offert.
Even for that 60% bump, that was after talking to 20 recruiters over the phone, 8 online code exams, 5 multi-stage interviews, and getting 2 offers, over an exhausting three week period, and juggling all those with a day job was super difficult, and I had to schedule enough of those during the work day that it got to the point where my former boss probably started to notice.
I'd hate to have to double, triple, or quadruple that effort just to get maybe a 30% bump if my previous salary was public knowledge.
I managed to get a significant salary bump even without having a job, because I made sure they understand from the beginning I'm happy to walk away.