Hi Venkata! While I’m not familiar with the Brown undergraduate research policies, I would definitely suggest meeting with an advisor within your major or potential major’s department, since different majors have different requirements/allowances for research for credit. Asking someone in your department is also more helpful in evaluating research opportunities outside of a standard school year lab experience. At the University of Michigan, the maximum amount of research credits is usually listed in the major requirements, so I would also check your major’s checklist. In my experience from two different colleges I attended/attend, two semesters of research is the maximum amount that can count towards a major’s lab requirement/upper level electives. Here are some links to common pre-med U of M majors and what the departments say about research:
Neuroscience 
Biology
Chemistry
Physics
Pre Health Page
Regardless of what your major allows, I encourage you to participate in research as much as you can! It doesn’t have to be in a pre-med-esque department either. Research something you’re passionate about! The experience is much more attractive to health career schools if you can speak meaningfully about it in interviews. In the end, the purpose of research in undergrad is to demonstrate and apply what you learn in courses (helpful in displaying competency to health schools) and to deepen your understanding of the field. If you have the credits for it and are in a good place with other requirements, I find that it helps to take research for credit anyway, even if it doesn’t count, during the school year because then you have large, regular chunks of time built into your schedule—otherwise you might be scrambling to find time with a full class schedule and extracurriculars. Good luck with your research and the up coming school year!