I am sorry. But, even though visas are involved, this is not an immigration question.
With that said, you should try to find a 'real' employer ... these "job shop" employment arrangements seem to regularly be problems for the worker.
I will re-classify as an employment law question.
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I could not agree more. Mr. Capriotti has summed it down to what it seems. H-1B requires a bona fide employer-employee relationship. If you are merely looking for someone to run your pay roll, the H-1B petition is unlikely to fly with the USCIS and later at the visa interview.
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For purposes of this Answer, and although it may be an issue, let's put aside the issue of your H1 visa and the requisite employer sponsorship.
From a non-compete perspective, yes, at least in Illinois there could be an issue. From the facts you recite, it seems it is your plan and intention to compete with Employer A and to indirectly sell or market services to the Client. That is what the terms you recite expressly forbid. The full terms of the non-compete/employment agreement would be helpful to assess its overall validity and strength. It would also help to know additional facts, such as whether or not your role with A included access to information about Client, or work involvement with Client; and what is the geographic distance of A from Client, and did D have a prior relationship with Client, even indirectly?
The ability to navigate work within the confines of a non-compete agreement requires particular legal knowledge. Choose an attorney wisely and be sure to consider the impact any actions you undertake will have on your residency status. Many of us have colleagues skilled in immigration law for consultation on such issues. Even your new employer, D, can be dragged into the mix if A decides to assert rights to prevent D from utilizing your knowledge and relationship to "compete" for Client's business.
I hope this helps!
John R. Malkinson/ Malkinson & Halpern, P.C.