The facts of this case are extremely complicated and the simple fact that you have had litigation around this issue makes it practically impossible to answers these questions in this forum. There are simply to many facts and to many documents not available. I would recommend you use the find lawyer tab above to locate a lawyer in your area. Many lawyers offer free consultations where you can gain a better understanding of your legal rights. You can also go back to the lawyer that represented you on the non-compete. Good Luck
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Assuming I understand your situation correctly, it would not appear that you have any standing here because you are not privy (again I assume) to the contracts in question. That is, even though their action may have an affect on your business, unless they own you some duty to refrain from that I cannot see how you will have standing to bring the action. I would think that the doctors they are contracted with will be able to take action on account of their breach assuming it amounts to that.
Of course, there is only so much insight one can offer without knowing more. You should consult a lawyer in private to discuss in more detail.
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I suggest that you consult an attorney who is ecperienced in this area law. The attorney who represented you in the prior litigation is in a good position to advise you. It sounds like tortious interference but more information is needed. Sgain, the attorney who previously represrnted you would have much of the needed information.
Advice given by me in this space is for educational purposes only. Advice given by this attorney constitutes legal advice only if a contract is first signed by this attorney and the client/questioner and a fee is paid to this attorney for such advice.