To my knowledge critical realism theorists especially from Frankfurt School would help you how to analyze philosophical assumptions in your study. I would recommend that the authors such as Jurgen Habermas (1986), Jacque Derrida (1979), Michele Foucault (1972) would provide you with more than enough sources on how to apply philosophical assumptions in your analysis. Other authors from the similar academic circle would also be helpful. You can also refer to the works of Roy Bhaskar (1997), well-known for explanatory critiques, and his followers such as Norman Fairclough (2003) and Ngai-Ling Sum (2013). If your study focuses mainly on linguistic analysis, e.g. speech acts, presupposition, then the books by Stephen Levinson (1983) and Paul Grice (1989) would be excellent sources. Please keep in mind that all the books by these authors are far from easy.

Thembela Nokela , I'm not sure what your study is or what domain you are trying to apply philosophical assumptions to, but I have read a little bit about interpretivist approaches to research as they apply to education (for me, specifically translator education). Some of the key scholars who write on this in the field of translator education are Don Kiraly, Gary Massey, and Sascha Hofmann.

They mainly look at concepts such as action research, and have been approaching most everything through I guess what might be a branch of interpretivism called "pragmatism." As applied to education, Kiraly describes this as looking for a variety of pragmatically useful (good for the time being) ways to improve and innovate the way he teaches or facilitates learning. It's not about finding the ultimate, singularly correct way of teaching. It's about exploring different approaches that you suspect will be better than your current approach. He writes a lot about abduction (as opposed to deduction or induction). Basically abduction is about digging up new hypotheses based on what you think will be likely solutions to a problem you are facing.

So on to the authors that these philosophical approaches (pragmatism, abduction) are based on. They cite American pragmatists like Charles Peirce, John Dewey, and William James. Peirce is linked specifically to the scientific investigative process of abduction. Kiraly later links abduction to the research methodology of action research, which he traces to German-American psychologist Kurt Lewin.

If you'd like to read more about where I got the above information from, it mainly comes from:

Massey, G., Kiraly, D., & Hofmann, S. (2018). Beyond teaching: Towards co-emergent praxis in translator education. In Translation–Didaktik–Kompetenz (pp. 11–64). Frank & Timme.

You might also look at:

Peirce, Charles S. (1903) Harvard Lectures on Pragmatism. CP 5.171–5.204

Peirce, Charles S. (1931–1958): Collected Papers of Charles Sander Peirce. Hartshorne, CHarles/Weiss, Paul [eds.]: volumes 1–6/Burks, Arthur: volumes 7 and 8. Cambridge MA: Belknap Press.

Adelman, Clem (1993): "Kurt Lewin and the Origins of Action Research". In: Educational Action Research 1 (1), 7–24.

Reichertz, Jo (2009): "Abduction: The Logic of Discovery of Grounded Theory" [39 paragraphs]. In: Forum Qualitative Sozialforschung/Forum: Qualitative Social Research, 11 (1), Art. 13.

I think that every single area of study has its own way of making assumptions and then those assumptions are approved, rejected or refuted. The best way to have an idea about this is to study the most recent and most relevant theory with regard to your area of study. There you will find much of the discussion.