The situation in which the magnitude of the total force is greater than the magnitude of each of the individual forces is when four people stand on each side of a large box, and all four people push the box with the same amount of force.
In this case, all the forces add together in the same direction, resulting in a total force that is greater than the force exerted by any individual person.
In contrast, when one person pulls while another pushes in opposite directions, the forces will effectively reduce each other's impact, resulting in a smaller total force.