Rule 101 for an outsourcer is getting payment for everything as per the contract, and charging extra (and at a premium) for anything above and beyond.
Having been outsourced in the past, I know from first hand experience that former colleagues used to you going the extra mile when we were all on the same side, don’t take it well when your new boss in the outsourcing company actively prevents you from doing so without extra payment agreed in advance.
Another reason why the ‘pulling out the stops’ behaviour of the 70s argument advanced above is rarely relevant to the real world of 21st century business.