While complexifier doesn't show up in most English dictionaries, you can use it to mean "a complicating factor." No matter how much you love rabbits, keeping eight of them in your apartment will be a real complexifier for you.
You might use this colloquial word when you're trying to sum up the idea of "something that makes things extremely complicated." If moving to a remote island has made your life more difficult and convoluted, that's a complexifier. Other complexifiers might include living without electricity, taking on a big responsibility at work, or adopting a blind dog, for example. At the heart of complexifier is complex, "complicated, intricate, or consisting of many parts."