A railroad flatcar is initially at rest. It holds N people each of weight ]\\\\I. If each person in succession runs parallel to the tracks with a relative velocity Vre1 and jumps off the end, do they impart to the car a greater velocity than if they all run and jump at the same time?

If each person in succession runs parallel to the track with relative velocity v_rel and jumps to the end, they do not impart greater velocity to the car compared to a situation in which they all run and jump at the same time. It is important to note that when all the people jump simultaneously, they impart a linear momentum to the car, which is equal in magnitude to the sum of their individual momentum but in the opposite direction.
However, when they jump, the effective mass of the train reduces by a larger amount, and the decreased inertia allows car to gain a higher momentum.
When persons jump individually, the decrease in inertia of the car is not large enough to give it a higher velocity relatively.