We present in this paper two novel concepts of hybrid metamaterials that combine a core unit cell of re-entrant or cross-chiral shape and lateral missing ribs. The first topology is a hybrid between an anti-tetrachiral and a missing rib (cross-chiral) configuration; the second one has a variable cross-chiral layout compared to the classical missing rib square structure. Their in-plane mechanical properties have been investigated from a parametric point of view using finite element (FE) simulations. The two classes of metamaterials have been benchmarked to obtain optimized designs and specific effective properties. Nonlinear simulations and experimental tests of the new re-entrant missing rib metamaterials featuring optimized geometry parameters have been performed to understand the behavior of these architectures under large deformations.