Is it possible to create a mutual relationship between full-time work and a PhD program?
It is not unheard of to have people work outside of an academic setting on their PhD thesis. For instance, in the US national laboratory system, there are a number of graduate students working on their PhD thesis. It's not a large number—maybe a dozen or so per laboratory—but it's not zero, either. In countries such as Germany and the Netherlands, it is also not uncommon to be employed as a PhD student in industry; however, the financing of that is somewhat unclear to me. (They may receive the equivalent of their stipend, or they may receive a "professional" salary.)

That said, I suspect it will be difficult to find an arrangement which will allow you to work full-time and receive both a graduate stipend and a full-time salary. Such arrangements would be generally frowned upon by both university and the external sponsor.