We report the quaternary Heusler compound derivatives CoFe1+xTi1–xAl and CoMn1+xV1–xAl, which do not have centers of inversion. Classical T2T′M (T, T′ = transition metal, M = main group element) Heusler compounds (prototype: Cu2MnAl) crystallize in the L21 structure, space group Fmm (225) that exhibits a center of inversion. Replacing one of the T2 atoms by another transition element (T″) results in a quaternary TT′T″M compound with F3m symmetry (Y; structure type LiMgPdSn) without center of inversion. In the case of “quasi closed shell” compounds with 24 valence electrons in the primitive cell, one expects the absence of ferromagnetism according to the Slater–Pauling rule. Increasing the number of valence electrons will allow a study of the onset of the magnetic ground state. In this work, CoFeTiAl and isovalent CoMnVAl as well as the accompanying solid solutions CoFe1+xTi1–xAl and CoMn1+xV1–xAl were synthesized and their structure and magnetic properties investigated. CoMn1+xV1–xAl (x > 0) is a half-metallic ferrimagnet in which the magnetic ground state is controlled by the strong localized moment at the Mn atoms replacing V.