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In the search for new single molecule magnets (SMM), i.e., molecular systems that can retain their magnetization without the need to apply an external magnetic field, a successful strategy is to associate 3d and 4f ions to form molecular coordination clusters. In order to efficiently design such systems, it is necessary to chemically project both the magnetic building blocks and the resultant interaction before the synthesis. Lanthanide ions can provide the required easy axis magnetic anisotropy that hampers magnetization reversal. In the rare examples of 3d/4f SMMs containing CrIII ions, the latter turn out to act as quasi-isotropic anchors which can also interact via 3d-4f coupling to neighbouring Ln centres. This has been demonstrated in cases where the intramolecular exchange interactions mediated by CrIII ions effectively reduce the efficiency of tunnelling without applied magnetic field. However, describing such high nuclearity systems remains challenging, from both experimental and theoretical perspectives, because the overall behaviour of the molecular cluster is heavily affected by the orientation of the individual anisotropy axes. These are in general non-collinear to each other. In this article, we combine single crystal SQUID and torque magnetometry studies of the octanuclear [Cr4Dy4(μ3-OH)4(μ-N3)4(mdea)4(piv)8]·3CH2Cl2 single molecule magnet (piv=pivalate and mdea=N-methyldiethanol amine). These experiments allowed us to probe the magnetic anisotropy of this complex which displays slow magnetization dynamics due to the peculiar arrangement of the easy-axis anisotropy on the Dy sites. New ab initio calculations considering the entire cluster are in agreement with our experimental results.