Can only one particle exist at a defined point in spacetime?

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.