It's possible to do this with just about any agency. I work with an LDS to supply gear and fills, and they happen to be PADI and SSI affiliated. They've also worked with independent NAUI instructors. The shop is happy to have foot traffic, regardless of instructor agency.I see it as a big advantage. I don't have to maintain billing, I don't own the rental equipment or pay for the maintenance thereof, I don't have to pay for the air fills used for teaching, I have a shop to get things from when something unexpected breaks, I have the support of other instructors to help me learn new skills and better ways of doing things. I still teach the classes that I want, when, and where I want. Effectively everything I do is made better by having the support of the LDS and I try to encourage my clients to shop there too.
But I technically teach for a University, and don't want to be tied to one shop.