First, let me clarify a couple of things for you.
Case studies are anecdotal in nature, and as such, they’re good for gaining insights into your data statistics. However, you cannot make accurate conclusions from case studies, unless they involve valid testing methods. You need empirical evidence for that kind of information.
The second point is to the specific example you cite. Search engines do not use domain extensions as a ranking factor, with the notable exception for Country Code extensions on localized results. So you won’t find any credible case studies that illustrate a difference that doesn’t exist.
If you are looking for a good website that does marketing experiments, not SEO per se, but certainly useful information, check out MarketingExperiments.com for lots of credible scientific-based case studies. I am sure that you can hire them to perform case studies as needed if they are related to marketing experiments and not just cargo cult science.