Is there a "limit" of how many mg of caffeine someone can have in a day? or no limit?

Yes but limit varies: Yes, there is a limit but that limit varies depending upon your metabolism and sensitivity. Some can't handle even the small amount of caffeine in a cup of coffee while others can down 5-6 cups/day. You'll know you've exceeded your personal limit if your heart races, your head pounds, you feel nervous & jittery, and you go through withdrawals when you miss your morning cuppa joe.

Yes there is a limit: But some people have enormous tolerance to it. However, it is really not good to take large doses of any stimulant, whether that is cocaine, amphetamine or caffeine, for most people. The higher the dose, the more likelihood of anxiety, insomnia, tremor and even severe reactions like psychosis and seizures. 2-3 servings per day, in the mornings, is the maximum most would recommend.