Is it possible for a high school senior to handle taking 3 AP courses?

Not at all, Im taking 4 ap classes (chem, literature, Stats, environmental science) my senior year. But you will be making a huge mistake if you take AP Bio and AP chem the same year. I dont know about your school, but ap bio and ap chem are the hardest classes you can take, and its not a good idea if you take them together. I separated them by taking ap bio my junior year and ap chem my senior year. Try dropping one of them, and taking an easier AP class.