As long as the doctors do not overlap, then you should be fine. But you are going to burn out fast. I would NOT try to sell my regular docs the 1099 products. That's really risky, especially if they ask and you happen to have a DM with you.
You better hope that if any of your "1099 docs" see you in a building with a DM for your "salaried job", they don't recognize you.