Yes. You can say "I'm sticking with you." Which means you are supporting that person's stance or endeavor. Or you could mean physically staying with that person. You may have been given an option to go somewhere else with another person, but your have decided to stick with your friend. I think a famous example is "Stick with me, kid, and you'll go far." You can also say "I'm stuck on you." This usually means you are infatuated with the person, maybe in love with the person.