It's a very bad idea to study multiple languages that are related to each other because you will mix up words (such as french and italian). It's also a bad idea to do it when you aren't at least semi-fluent in a non-native language yet; because the brain isn't adjusted to storing multiple lexicons.
If you absolutely want to study more than one, don't start a second until you are at least procient in the first to give the brain time to organize itself. I wouldn't recommend it
Also, keep in mind that you'll be required to study these languages your entire life. If you stop, you'll forget the language until you begin studying it again. The more languages, the more work required.
One recommendation I read before for learning multiple foreign languages is to learn them one by one, but through bootstrapping. That is to say, you start by focusing on a single language, call it L1. Once you're fairly confident with L1, you start learning the next language, call it L2. However, this time around, instead of using your native language to study L2, you learn L2 using material from L1, thus reinforcing both languages.
I've heard that Esperanto is a good starting point for learning languages, though I don't have any experience with it.