It's unlikely you will have the appraisal raised. The insurance companies USED to have you get at least two bids for the work, and they would pay based on that. However, there was rampant fraud based on that system. So now they imploy there "OWN" adjusters, who estimate the cost of repairs. If additional damage is uncovered during repair, they will usually make allowances to the estimate. The unfortunate thing is that they base their repair estimate on the absolute cheapest repair parts. You may be able to raise their estimate if you insist on better quality replacement parts (ie. GM OEM parts).