Actually, no, theoretically it shouldn't. There is a little thing called gravity that you seem to fail to consider.
Even if your friend had the physical strength to lift you, after having been lifted by you, his feet would immediately fall back to the earth as soon as your feet left it. Regardless of whether you can support the weight of each other, one or the other must be supporting the weight of both of you against Earth's gravity. Goes back to that whole action and reaction thing.
Or do you really think that once you lift your friend off the ground, he is going to magically be able to float in the air and lift you higher? Or that his internal lifting strength is somehow going to counteract the external influence of gravity?
It doesn't matter how much beefcake your friend eats; you're never going to escape Newton's laws.