You bring back memories, I have 3 daughters the eldest now 13 and the youngest 3. My eldest bit people with a passion at 2, I thought she was possessed I even took her to the doctors I was so concerned. It turned out that she was just so frustrated other people couldn't understand her needs and wants that she bit them, also being the first child she had difficulty in sharing so we really over emphasized sharing at home and bought her a book called 'Where the wild things are' , it is a story about a little boy who is so naughty he is sent to bed wtihout any supper and obviously we added extra words about biting to suit. It wasn't an overnight solution but it is an age that is very tough for a first born and he is obviously so desperate to be understood he can't wait or understand why other little people don't understand him when his closest 'grown ups' do. So my advice would be don't worry about the biting, concentrate on the sharing, even sharing cuddles and kisses as it can also be jealousy of not being the baby any more.
I now play a game with all of mine, telling them each they are my favourite, (like Bruce Forthsythe) the older two know it is a game but the younger one loves thinking she is the 'favourite' and our cuddles therefore mean more to her.
I am not super mum but give it a try, I have 3 kids I can take them anywhere so it worked for me, no naughty step in my house, he is not being naughty he is being misunderstood.
Best of luck!!