Is it advisable (or even possible) to get a second masters in a similar field from a higher-ranked instution? In May, I will graduate with a Master's Degree in Mathematics from a school ranked #201 in the U.S (for undergraduate education). It is unranked in graduate school rankings (for my program). 

I am excelling in my current program with research focus in mathematical biology.

My goal: I would like to get my Ph.D. from a top-5 institution. 

Assuming I don't succeed in my goal directly, is it advisable or even possible to pursue a second Master's degree in mathematical Biology, from a second-tier institution, and then apply for a Ph.D. at a top-tier institution?
It is possible to get second masters degree in a similar or related field. Doing so might even help with getting into a top PhD program.

That said, where you did your master(s) degrees is not the key to the kingdom or even the most important thing in your PhD application. Demonstrating that you are smart, hardworking, and excellent at research should be your goal. Another masters from a "better" University might help toward that end but it's hardly the only or best way.

Focus on doing excellent research, publishing that work in excellent scholarly venues in your field, and getting excellent letters of recommendation from people that are known and respected in the field. If you do those things, and if you also have good grades and test scores, you'll be a strong candidate for any PhD program. I have seen people build that portfolio as an undergrad, in a masters program, as research staff at a university, or even in industry. What you do matters at least as much as where you do it.