The Contractor has submitted a quote and the PM is reviewing the submission. The Contractor has now said there are more costs they want to add in, is this permissible?
Nothing to stop them doing it. If they have realised the quote was wrong they can submit a new one. The Project Manager can not exactly ignore it as if they can see the first quote was wrong they should have assessed it themselves and increase it if they saw it was too low.
Contractor says they want more cost. If I was the PM I would consider the merits/validity of both quotations and pay for the bits I agree or assess myself if i think any elements are not valid or over priced in accordance with the contract.