“Theories”/“frameworks” for how multiparadigmatic research should work (in the context of interdisciplinary research)? Interdisciplinary research is research generated from collaboration between people from different disciplines (or one person steeped in different disciplines). 

This can mean simply that the multiple disciplines have knowledge of different domains of the world, and integrate their knowledge without any “paradigmatic tension” (where paradigm is meant in the philosophy of science sense, e.g. Kuhn’s sense). For example, a biologist and a chemist may cooperate on studying the biochemistry of a bacteria. The chemist has more knowledge of the low level chemical interaction, while the biologist has more knowledge of the higher level structure. The researchers combine knowledge of different aspects of the system, but are roughly within the same paradigm.

However, for some disciplines, especially in the social sciences, different disciplines don’t merely have knowledge of different aspects of the system, but have different perspectives/frameworks for analyzing the same aspects of the system. There is some “paradigmatic tension”. For example, economists often use rational choice models, and may even apply them in contexts that would traditionally be seen as in the domain of sociology (e.g. there is a famous model of ethnic segregation using a simple mathematical toy model and rational choice). On the other hand, sociologists also study segregation but tend to use an entirely different methodology and philosophy. I think both approaches can generate meaningful insight about the phenomenon. interdisciplinary research between these two would I guess look somewhat different than that between a chemist and a biologist. The researchers not only have different knowledge about different parts of the (social) system, but also have different perspectives/approaches to analyzing a given aspect of the system. The researchers study perhaps overlapping aspects of the same system, but are doing so in different paradigms, which may have some tension between them

I am wondering: Have things been written about how to deal with this latter type of “multiparadigmatic” research? Are there  frameworks/philosophies for how to get such different types of disciplines to fruitfully work together?
Interesting question. My suggestion would be to look in the social and historical sciences for advice how interdisciplinary research can work fruitfully. The standards of methodology and reproducibility can vary very strongly from fields like engieenring to psychology so that researchers from both fields have a very hard time to find a common denominator apart from common vocabulary or measured quantities.

In the social psychology/historical sciences branch I'm aware of very fruitful interdisciplinary projects/collaborations and results that have been published.

Even phycisists study social systems, nonlinearity of complex systems, population growth models etc. So often interdisciplinary research seems to be worthwile to understand which and how distinct quantities in complex systems are scaling. Multivariate statistics is a common method here to understand the structure of complex systems by different perspectives and methods. But a common scientific language or method seems necessary, even if it is as simple as counting things in both disciplines and relate quantities to distinct phenomena. While machine learning algorithms are not very smart, they can show at least whre possible correlations or dependencies from perspectives of each discipline are.

There have been many tests by researchers to publish nonsense articles in journals of other disciplines, e.g. Sokal affair. So rather falsifications of multiparadigmatic/interdisciplinary research. 

I think a good place to look would be EU funding calls requiring interdisciplinary collaborators and setting up clear requirements and goals for the project results to get a picture what modern interdiscplinary research standards are.