Yes; a simple example is Norton's dome. It is possible to construct a frictionless curve such that a particle that is pushed up the curve with correct initial velocity will reach the top and halt in finite time. Observing a particle sitting at the top of the dome, there is no way to tell when it reached that point or from which direction.

It's not that "multiple pasts can exist", it's that "multiple pasts _would be sufficient to explain_ the effect that is being observed now".

E. g. "The apple hit Newton on the head" could be explained by:

1. The apple was hanging on the tree at `t - 1` and the wind shook it loose.

2. The apple was flying through the air because his mother threw it and it collided with his head

3. The apple spontaneously generated due to as-yet-not-understood quantum fluctuations 3 meters above his head.