I'd say a large overshoot of IV is possible in many companies, but unlikely to reach 2xIV nowadays in the case of Berkshire given Buffett and Munger's stated intention that they would seek to discourage extreme undervaluation or overvaluation so that incoming/outgoing shareholders do not benefit disproportionately from the misfortune of their counterpart in the trade. I think
Nonetheless there's a wide enough trading range to really load up when it's cheap and to lighten up when it's more fully valued. In my case, I last bought just under $125 (Feb 2016, which was <1.25x last reported BV at the time, and later turned out to be <1.2x BV at year end) but I sold a good chunk at a somewhat undervalued $140 (May 2016) to load up on Apple, which was extremely cheap at $95 at the time.
I'd have needed a much higher price to sell Berkshire and hold the cash, and so far that hasn't happened (except for a temporary need to 'demonstrate I had £X cash available to be withdrawn' for a one-off purpose a few years ago, which required me to sell a lot of my shares and show it had been in my account and available for withdrawal for a specified period, then I was able to buy back later).
If I had used borrowed money such as a mortgage extension to buy extra Berkshire (which I've not done yet but might consider in future at prices <1.3xBV) then I might be tempted to sell to cash at 1.55-1.60xBV to pay off the loan or lock in gains, depending on circumstances due to the different risk profile.