For your experience of the world to be superposed it would mean that you carry out a quantum experiment with two mutually exclusive outcomes |x> and |y> and you actually experience the superposed result |x>+|y>. This would be like opening the box in the Schroedinger's cat experiment and actually observing the cat to be |alive>+|dead>, instead of either alive or dead. Maybe it's possible, but such an experience has never been reported.
So it's "possible" but would never happen in a trillion lifetimes of the universe. You can tell the difference between that and "impossible" by watching the quantum mechanics work for a few isolated particles, and observing what it means for them to fall out of superposition equilibrium. But in practical terms, it's equivalent to impossible.