Sulfur-terminated single sheet (ss-)MXene was recently achieved by delamination of multilayered van der Waals bonded (vdW)-MXenes Nb2CS2 and Ta2CS2 synthesized through solid-state synthesis, rather than via the traditional way of selectively etching A-layers from the corresponding MAX phase. Inspired by this, we perform a computational screening study of vdW-MXenes M(2)CCh(2) isotypical to Nb2CS2 and Ta2CS2, with M = Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Mo, or W and Ch = S, Se, or Te. The thermodynamic stability of each vdW-MXene M(2)CCh(2) is assessed, and the dynamical stability of both vdW- and ss-MXene is considered through phonon dispersions. We predict seven stable vdW-MXenes, out of which four have not been reported previously, and one, V2CSe2, incorporates a new transition metal element into this family of materials. Electronic properties are presented for the vdW- and ss-forms of the stable vdW-MXenes, suggesting that the materials are either metallic, semimetallic, or semiconducting. In previous experimental reports the vdW-MXene Nb2CS2 is synthesized by manipulation of the corresponding M(2)AX phase Nb2SC. Therefore, we also evaluate the thermodynamic stability of the corresponding M(2)AX phases, identifying 15 potentially stable phases. Six of these are experimentally reported, leaving nine new M(2)AX phases for future experimental investigation.