A crossmember arrangement for reinforcing a motor-vehicle body includes a crossmember for dissipating loads in the Y direction, an intermediate piece, which is connected directly or indirectly to the crossmember and is intended for fastening the crossmember to a supporting pillar, in particular a B pillar, and a fastening body, which is connected to the intermediate piece and is intended for butting with surface-area contact against the supporting pillar. The fastening body is configured in the form of a chamber profile which runs predominantly in the Y direction. Dissipation of high loads in a motor-vehicle body is made possible, along with straightforward installation capability of the crossmember arrangement in the motor-vehicle body, as a result of the fastening body of the crossmember arrangement, the fastening body is configured in the form of a chamber profile, running essentially in the Y direction.