The answers to this question might give some insight into the matter. https://www.researchgate.net/post/Why_choose_mix_methods_for_social_sciences

Mixed methods research is largely as approach to collecting and analyzing data, and as such it does not require any single ontological and epistemological paradigm. Among the paradigms that have been used in association with mixed methods, two of the most common are pragmatism and critical realism.

These issues are routinely discussed in textbooks on mixed methods, such as Creswell and Plano-Clark.

You can find all what you want on Mixed methods research in many books, particularly, the following book:

Creswell, J. W. (2017). Research design: Qualitative, quantitative, and mixed methods approaches.5th eds. London: Sage.

In addition to the above book, I published a paper on mixed methods research in the filed of sport leadership, it may give you an idea about what you are looking for.

Megheirkouni, M. (2018). Mixed Methods in Sport Leadership Research: A Review of Sport Management Practices.Choregia, 14(1). pp. 1-20.

Pragmatism recognises that there are a plethora of different methods of interpreting the world and how people live. As a result there are multiple realities and research methods should reflect this. Willig (2008, p. 22) states ‘Strictly speaking, there are no ‘right’ or ‘wrong’ methods. Rather, methods of data collection and analysis can be more or less appropriate to our research question’. Therefore, qualitative, quantitative or mixed methods are open to pragmatists. Indeed Johnson and Onwuegbuzie (2004) and Denscombe (2007) suggests pragmatism is ideally suited to mixed methods and was therefore chosen as the most appropriate for this study.

The mixed method research in social sciences embeds in Pragmatic / Realist or Realism as a philosophy of research which, believe the form and nature of reality is not the absolute unit (Ontological viewpoint). Consequently, it is recognized from both positivism and interpretivism positions (Epistemological viewpoint). Therefore, one’s should follow its principle (Axiology) to apply that to the Qual. and Quan. research strategy as a mixed method paradigm (Methodology). And lastly, express that to the most appropriate language and voice (Rhetoric) to the audience.

Contributors may find the paper below of interest.

Essentially, the ontological/epistemological viewpoint of mixed method research is that an adequate explication of 'the social' can only be had using both quantitative and qualitative methods.

I disagree with the idea that "the ontological/epistemological viewpoint of mixed method research is that an adequate explication of 'the social' can only be had using both quantitative and qualitative methods."

Instead, I would say that mixed methods can sometimes provide a better answer to a research question than using either quantitative or qualitative methods alone, but that depends on the research question.

In other words, mixed methods is about methods, not about a unique approach to ontology and epistemology.

I concede that my previous post should have said "sometimes" rather than "can only be had".