“Theories”/“frameworks” for how multiparadigmatic research should work (in the context of interdisciplinary research)?
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.