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We describe magneto-, baro- and elastocaloric effects (MCEs, BCEs and eCEs) in materials which possess both discontinuous (first-order) and continuous (second-order) magnetic phase transitions. Our ab initio theory of the interacting electrons of materials in terms of disordered local moments (DLMs) has produced explicit mechanisms for the drivers of these transitions and here we study associated caloric effects in three case studies where both types of transition are evident. Our earlier work had described FeRh's magnetic phase diagram and large MCE. Here we present calculations of its substantial BCE and eCE. We describe the MCE of dysprosium and find very good agreement with experimental values for isothermal entropy ($ΔS_{iso}$) and adiabatic temperature ($ΔT_{ad}$) changes over a large temperature span and different applied magnetic field values. We examine the conditions for optimal values of both $ΔS_{iso}$ and $ΔT_{ad}$ that comply with a Clausius-Clapeyron analysis, which we use to propose a promising elastocaloric cooling cycle arising from the unusual dependence of the entropy on temperature and biaxial strain found in our third case study - the Mn$_3$GaN antiperovskite. We explain how both $ΔS_{iso}$ and $ΔT_{ad}$ can be kept large by exploiting the complex tensile strain-temperature magnetic phase diagram which we had earlier predicted for this material and also propose that hysteresis effects will be absent from half the caloric cycle. This rich and complex behavior stems from the frustrated nature of the interactions among the Mn local moments.