An elementary particle can indeed be in multiple places at the same time, except when it interacts with something “classical”: an instrument, a cat, a video camera, a human, a rock, something that confines that particle to a “position eigenstate”.
But which position eigenstate? Well, that’s where the wavefunction comes in: every one of those places that the particle can be gets assigned a probability.
Now if one particle can be in two places at once, so can a system consisting of a pair of particles. Or a system of a hundred particles. But when we work out the probability of this hundred-particle system being in a “position eigenstate,” we find that nearly all positions will have vanishingly small probabilities.
And when we increase the number of particles further, for instance, to the insane number of particles that a human being consists of, we find that apart from the one-and-only position of that human being that classical physics predicts, all other positions will have probabilities so tiny, you will never observe them.
In fact, such a multiparticle system behaves in a way that is itself indistinguishable from something “classical”: So not only will a human being (or a cat, or an instrument, anything that consists of a large number of uncorrelated quantum particles) always be in a position eigenstate, things that human being or object interacts with will also be, most of the time.
And thus the classical world is born, because all that quantum-ness gets averaged out, so to speak, when very large numbers of particles are involved. The principle is still there, but the probabilities assigned to anything not predicted by the classical theory are so astronomically small, it is a dangerous understatement to say that it will never happen in the lifetime of the universe or even the lifetime of a zillion universes.