A new double double perovskite of ideal composition CaMnCoWO6 has been synthesised at high pressure. The structure is tetragonal (P42/n, a = 7.6651(3), c = 7.6822(3) Å) and disorder between A-site Mn2+ and B-site Co2+ leads to a Co-rich off-stoichiometric composition CaMn0.8Co1.2WO6 [Ca(Mn0.65Co0.35)(Co0.86Mn0.14)WO6]. An unusual combination of commensurate and incommensurate spin orders (Mn-site spins with propagation vector (0.5 0.5 0.5) and Co-site spins with (0.5 0.42 0.5)) is observed below a magnetic transition at TC = 18 K. This is the first discovery of complex magnetism in the double double perovskite family. Data relates to the publication Data for publication K. Ji, R. Chen, P. Manuel, J.P. Attfield (2023). "Coexisting commensurate and incommensurate magnetic orders in the double double perovskite CaMnCoWO6", ZAAC ( https://doi.org/10.1002/zaac.202300047 ).