Doesn't work well or not at all

I have a multi-site currently set up as sub-directory. It is a non-profit that helps militry veterans and has multiple programs. What I want to be able to do is set up each program as a subsite with domain mapping(no problem) but then create corporate sponsor sites under each program with the URL connected to the program (subsite) not the main site.

I was hoping that I could accomplish this with Multi-Domains in conjunction with Domain Mapping. The installation instructions says that multi-domains is for sub-domains structure rather than sub-directory – but then says it doesn’t work “well” with subdirectory. Does that mean not at all? What can I do with the current structure to accomplish goal?