In "Babel No More" the literature on hyperpolyglots is reviewed.
I'm going from memory, but he said the most languages you'll find people using every day in a community is about 6. In some places where this happens, like India, this can be less impressive than it sounds because the speakers, to some degree, homogenize the grammar across the languages they speak, which are typically similar to begin with.
For individual instances of hyperpolyglots, the number of languages known is a slippery metric, people mention numbers of languages known between 7 and 100. Even the best hyperpolyglots usually do a refresher to be able to resume using them and they spend stupendous amounts of time studying. Given that they need to spend so much effort on study makes me think that's the main limit.
Sciencewise, there just aren't a lot of these people and some of the more famous ones are dead, so I wouldn't expect a lot of scientific data on them for a while.