Not without passing places, because you can't miss a stop without the train in front of you also missing it, at least without an eye watering body count.
Depends on how closely you are trying to run those trains! If they are both skipping every other stop, they will both have the same mean speed, and thus shouldn't have to pass one another if there is sufficient initial spacing.
For example, in the simple case where the stations are evenly spaced, if train B arrives at station 1 at the same time that train A arrives at station 2, then they will leave at the same time and arrive at stations 3 and 4 respectively at the same time, and never catch up with each other.
