In this work, we demonstrate experimentally the remarkable DC magnetic screening ability of hybrid superconducting screens. The configurations under investigation combine a 30 mm-diameter disk-shaped superconducting bulk, or another with a 10 mm-diameter hole, with different closed superconducting loops made from coated conductors. The loops are placed coaxially with the bulk. The bulk superconductors and the closed-loop coated conductors are made of GdBa2Cu3O7 and the experiments are performed in liquid nitrogen (77 K). The DC and inhomogeneous field to be screened is produced by a bespoke coil and reaches around 100 mT at the location of the superconducting bulk, which is much less than its full-penetration field. By mapping the magnitude of the flux density using a 3-axis cryogenic Hall probe, we show that such a hybrid superconducting screen allows the maximum shielding factor SF above the bulk to be almost doubled. For the best investigated hybrid configuration, the SF reaches ~45 at 2.7 mm above the bulk. In addition, the area of the spatial region for which less than half of the applied field remains (SF > 2) is roughly multiplied by 4 when compared to a situation involving only a disk-shaped bulk. In this work, this region corresponds to a 60 mm-diameter circle. The choice of the loop diameter is found to result from a trade-off between maximum SF and extension of the screened region. Finally, we detail why these hybrid configurations bring such improvements: the key point is that the flux lines generated by the source coil are diverted by the bulk towards a region where the closed-loop coated conductors can oppose the best to them.