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Suspensions of soft and highly deformable microgels can be concentrated far more than suspensions of hard colloids, leading to their unusual mechanical properties. Microgels can accommodate compression in suspensions in a variety of ways such as interpenetration, deformation, and shrinking. Previous experiments have offered insightful, but somewhat conflicting, accounts of the behavior of individual microgels in compressed suspensions. We develop a mesoscale computational model to probe the behavior of compressed suspensions consisting of microgels with different architectures at a variety of packing fractions and solvent conditions. We find that microgels predominantly change shape and mildly shrink above random close packing. Interpenetration is only appreciable above space filling, remaining small relative to the mean distance between cross-links. At even higher packing fractions, microgels solely shrink. Remarkably, irrespective of the single-microgel properties, and whether the suspension concentration is changed via changing the particle number density or the swelling state of the particles, which can even result in colloidal gelation, the mechanics of the suspension can be quantified in terms of the single-microgel bulk modulus, which thus emerges as the correct mechanical measure for these type of soft-colloidal suspensions. Our results rationalize the many and varied experimental results, providing insights into the relative importance of effects defining the mechanics of suspensions comprising soft particles.