What is the law regarding paying for uninsured losses over policy limits?

You may want your insurer to pay the exccess losses and seek reimbursement, but they don't have to do so. An insurance policy is a contract; the parties to that contract have to honor its obligations--no more and no less. Therefore an insurer is only required to pay up to the limits of its policy or coverage. You can certainly sue the building only or other responsible party (e.g. a sprinkler company which did improper or negligent installation or maintenance) for losses over the covered amount, but that's something *you* have to do if you deem it worthwhile, given the magnitude of uncovered losses, the cost of the lawsuit (e.g. attorney's and expert witness fees), and the perceived likelihood of winning.