Multicaloric driving — the simultaneous or sequential use of two thermodynamically distinct stimuli — has been applied to magnetostructural alloys and to multiferroic oxides, but not, to our knowledge, to a mixed-spin ferrimagnetic nanostructure, whose caloric analysis has so far stopped at the field-driven entropy change. That is the gap addressed here. A solid hexagonal core–shell nanowire built from nineteen atomic columns — a central column and a hexagonal ring of six, all of spin 7/2 (a Gd3+-like core), surrounded by twelve columns of spin 3/2 (a Cr3+-like shell) — is described by a mixed-spin Blume–Capel Hamiltonian and solved within the Bogoliubov–Peierls variational mean-field approximation. The geometry is engineered so that the sublattice moments nearly cancel, M(0) = +0.342, guaranteeing a compensation temperature tcomp = 3.489 below the ordering temperature tC = 5.404. Treating the core single-ion anisotropy as a second caloric stimulus alongside the magnetic field, we compute the isothermal entropy changes of field-only, anisotropy-only, and combined protocols, the adiabatic temperature changes, the order-of-operations (sequential) decomposition, and the RCP and TEC(10) figures of merit. Two qualitative results emerge. First, the synergy function Λ(t) separating the combined response from the sum of the individual ones changes sign discontinuously inside the compensation region, at the field-driven first-order reversal that occurs at t = 3.27, revealing an antagonistic-to-cooperative crossover anchored there. Second, the core anisotropy acts as a two-sided on/off switch for compensation itself: a compensation point exists only for −0.40 ≤ dA ≤ +0.35, being pushed to zero temperature at the lower edge and absorbed into tC at the upper one, while tC varies by only about 15% across the whole range. Multicaloric operation yields the largest adiabatic temperature change (ΔTad = +3.60 against +1.93 and + 1.50 for the single stimuli) and the best broadband figure of merit, TEC(10) = 0.135 kB per site, while peak-based measures remain dominated by the anisotropy channel alone (RCP = 1.158 against 1.151 and 0.339).


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