Can only one particle exist at a defined point in spacetime? And for the contrasting question, may two or more particles be superimposed at the same point in spacetime?
 A: A particle isn't located at a point. Particles are always delocalised over a non-zero volume of space, so while the expectation value of a particle's position is a point, the particle is not located at that point.
For a particle to be located at a point its wavefunction would have to be an eigenfunction of the position operator, i.e. a Dirac delta, but these functions are not well defined. For example they have an infinite uncertainty in momentum.
So the question would be better phrased as whether two particles can have wavefunctions that completely overlap, and the answer is that yes they can. The only restriction comes from the exclusion principle, which tells us that two fermions cannot occupy the same quantum state, but two particles can overlap without being in the same state. For example two particles travelling at right angles to each other could completely overlap.
A: If we consider the wavefunction of your particle the particle is at every instant at a definite point in spacetime. This point though is constantly changing randomly (unpredictable) within the confines of the wavefunction and this random changing is "concentrated" there where the absolute value of the squared wavefunction (which gives the probability of finding the particle) has the highest value(s). When we make a position measurement we measure a range around the position (a precise measurement is impossible) where the particle finds itself at the time of the measurement. This is not the standard Copenhagen interpretation which states that the act of the measurement determines the (range of) position(s), without the particle having a definite position before the measurement. But it's a valid interpretation. God does throw a dice (as you probably know, Einstein said that god does not play dice), but already before the measurement.
The same holds for two particles (let's say they are identical bosons to avoid the exclusion principle) whose wavefunctions find themselves in a superposition. The particles always find themselves at a definite point in spacetime but are randomly changing in accordance with the wavefunction. I think it's clear that the two particles will never find themselves at the same point in spacetime.
