Not much of import. One can always analyze the trends in the philosophical literature and possible explanations for them using methods in the social sciences, use clustering & classification algorithms to mathematically categorize philosophical literature along some n dimensions (including 1), or any number of similarly trivial scientific research projects.
Far more important and interesting is the philosophy of science. This is where philosophers and scientists are most likely to interact and produce that which is of value. A fair amount of scientific research is routine, procedural, and quite limited in scope as well as accuracy. What the sciences are, how scientists should understand the methods they use, and similar fundamental questions belong to a interdisciplinary domain of historians of science, philosophers of science, and scientists. Questions like the relationship between theory and hypothesis, the infamous Kuhnian paradigm shift, and even the extremist position of Feyerabend on scientific epistemology are all topics that are more answers to the question "which aspects of the sciences are suitable for philosophical study" and the question you ask.
To the extent there are aspects of philosophy important to science (and I absolutely believe there are), these are not really subject to scientific research. Rather, they concern scientific research and allow philosophers to help scientists think outside of the box (and lab) about what it is they do, and inform philosophers as to the nature (the process, nuances, and other components) of scientific research.
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