Bumper cross member system for a motor vehicle, modular system, and motor vehicle having such a bumper cross member system

A bumper cross member system for a motor vehicle, the cross member system having a base structure comprising:

• a bumper cross member that extends in a post-assembly position transversely relative to the vehicle,
• a first crash box and a second crash box, wherein, in the post-assembly position, the first crash box and the second crash box extend rearwardly from the bumper cross member longitudinally relative to the vehicle, and
• at least one add-on-element configured on the base structure, wherein:
• the at least one add-on-element comprises a first crash box extender element and a second crash box extender,
• the first crash box extender and the second crash box extender extend forwardly from the bumper cross member in the post-assembly position forwardly longitudinally relative to the vehicle in such a way that an extended base structure having an elongated crash box is obtained,
• a profile cross section of the first crash box and a profile cross section of the first crash box extender:
• are serially disposed longitudinally relative to the vehicle, and
• completely overlap transversely relative to the vehicle to form a first common effective path extending longitudinally relative to the vehicle, and
• a profile cross section of the second crash box and a profile cross section of the second crash box extender:
• are serially disposed longitudinally relative to the vehicle, and
• completely overlap transversely relative to the vehicle to form a second common effective path extending longitudinally relative to the vehicle.