Interesting study! I can imagine something like a detailed concept map outlining the various factors affecting uptake of ART among HIV/TB co-infected patients.
I like that you plan to interview a wide range of stakeholders, and think that will make your data very rich. What would you think about adding a few patients/clients? They may highlight some barriers that providers may be unaware of, though I think sampling patients at each facility would be prohibitive, so maybe identifying one or two facilities where you could interview 3-4 patients would be interesting.
And related to sample size, maybe we'll talk about that more in class, but I think it depends on your analytic approach, as well as how common your themes are (e.g. if you are planning on collecting data until "thematic saturation")? A few weeks ago I found an article that was looking specifically at sample size in qualitative studies, and it came up with an estimate of 30-50 interviews to achieve thematic saturation for grounded theory. That being said, because you are interviewing a wide variety of types of people, I imagine you will uncover many themes from different perspectives, so I suspect you'll have to err on the side of more interviews to capture most of the important barriers. A strength, though, is that barriers that come up from multiple perspectives are likely to be significant, and may lead to a bigger impact if those barriers are addressed.