Just to add, a friend and colleague of mine was the #2 doctor at a state institution and was hopeful he'd take over as the chief clinical officer within a few years. He was sued, and the hospital didn't do anything to protect him despite that they gave us contractual promises that they'd cover our malpractice.
He left that job in disgust, and while he never told me the specific reason why, everyone we mutually know told me it was due to the lawsuit, where he had to shelve out quite a bit of money to pay for a lawyer that malpractice coverage was supposed to have paid, and while he did not lose the case, he could have, and because he had no coverage, he could've lost everything in his bank account.
If you already have malpractice insurance and tell the insurance company you're doing some extra work here and there, they will likely not add much to your annual fee. At least that's what happened to me. I worked at one place, had my malpractice insurance. I did some extra side work and the insurance company told me they would cover me for that too and not charge me anymore.