Ni-Co-Mn-Ti all-d Heusler alloys are attracting considerable attention for solid-state caloric-cooling applications due to their promising combination of excellent caloric and mechanical properties. Here, we report on the maximum attainable magnetocaloric effect in Ni37Co13Mn34.5Ti15.5, which shows a first-order magnetostructural martensitic transformation around room temperature. Heat capacity measurements reveal a giant transition entropy change of 43.5J(kgK)\\protect \\relax \\special {t4ht=−}1 and are utilized to estimate the magnetocaloric effect as well as the magnetic fields required to saturate it in isothermal and adiabatic conditions. Confirming the results based on this approach, we achieve maximum isothermal entropy changes and directly measured adiabatic temperature changes of 37.8J(kgK)\\protect \\relax \\special {t4ht=−}1 and -20.2K, respectively. Thus, the herein reported maximum attainable magnetocaloric effect outperforms classical Ni-Mn-based Heusler alloys, such as Ni(-Co)-Mn-In. Especially the saturated adiabatic temperature change surpasses all previously published values of magnetic field-induced first-order phase transitions measured around room temperature in pulsed magnetic fields in recent years. Thereby, we demonstrate that Ni(-Co)-Mn-Ti Heusler alloys are particularly suitable for the application of sufficiently large external stimuli to fully induce the phase transition and exploit their intrinsically large caloric effect.