Biting is super common among kids this age. Not all kids bite, but it isn't unusual. It does seem strange that your son is getting bitten this often or the "target" in all of these different situations. I tend to agree with Beth and wonder if he's a huggie child or if he's got some characteristic that makes him a more common target.... it isn't unusual for a biter to bite the same child more than once, but I do think it's strange that you've moved him from facilities and it still is happening.
My son was a biter as a young toddler and I have had kids in my care who are (have been) biters. It's terrible on both sides... when your kid bites someone or your kid gets bitten. What I have witnessed is that kids bite for a variety of reasons. Many times in play situations, it is when they are frustrated and can't use words to express their needs, or have poor impulse
control... they want a toy someone else has, they bite or they have a toy someone else wants and they bite. It happens in a second, and the most that the provider can do is what you say your new care provider is doing (shadowing, and using preventative measures)... or they ask them to leave. I know care providers that won't provide care for a child after one bite. It's not what I do, but some people feel that the home environment need to handle it before kids are in care and it's not their job to "cure' biting, but to protect the other kids... to each his own.
Good luck~ it's a common developmental phase for some kids and it doesn't last long. Hopefully it will resolve soon :(