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Spinel oxides are an ideal setting to explore the interplay between configurational entropy, site selectivity, and magnetism in high entropy oxides. In this work we characterize the magnetic properties of the spinel (Cr,Mn,Fe,Co,Ni)$_3$O$_4$ and study the evolution of its magnetism as a function of non-magnetic gallium substitution. Across the range of compositions studied here, from 0% to 40% Ga, magnetic susceptibility and powder neutron diffraction measurements show that ferrimagnetic order is robust in the spinel HEO. However, we also find that the ferrimagnetic order is highly tunable, with the ordering temperature, saturated and sublattice moments, and magnetic hardness all varying significantly as a function of Ga concentration. Through x-ray absorption and magnetic circular dichroism, we are able to correlate this magnetic tunability with strong site selectivity between the various cations and the tetrahedral and octahedral sites in the spinel structure. In particular, we find that while Ni and Cr are largely unaffected by the substitution with Ga, the occupancies of Mn, Co, and Fe are each significantly redistributed. Ga substitution also requires an overall reduction in the transition metal valence, and this is entirely accommodated by Mn. Finally, we show that while site selectivity has an overall suppressing effect on the configurational entropy, over a certain range of compositions, Ga substitution yields a striking increase in the configurational entropy and may confer additional stabilization. Spinel oxides can be tuned seamlessly from the low-entropy to the high-entropy regime, making this an ideal platform for entropy engineering.