So the 60-day grace period wouldn't apply meaning that you would have to leave the US and then reenter to start working for your new H-1B employer. And if this

So the 60-day grace period wouldn't apply meaning that you would have to leave the US and then reenter to start working for your new H-1B employer. And if this period of time after the 60-day grace period went on for a while, it could impact your ability to get visas in the future.