Hypothesis: Soft microgel colloids can be densely packed since particle networks can compress and interpenetrate. This evolution of the particle's internal structure associated with packing is expected to determine the linear viscoelastic properties and the yielding behavior of dense suspensions of microgel colloids. Experiments: We investigated the volume fraction-dependent linear and non-linear rheological response of suspensions of soft core-shell particles formed by a poly(N-isopropylacrylamide) (PNIPAM) microgel core and a thin poly(ethylene glycol) (PEG) shell. Findings: The linear viscoelasticity of suspensions reveals a transition from a fluid to a jammed glass state. Increasing volume fraction within the jammed state, the linear storage modulus and the yield stress show distinct regimes associated with the evolution of particle contacts, which involve progressive compression and interpenetration of the shell and core. The yielding of jammed suspensions occurs in two-steps: At small strains jammed cages are rearranged, while full disentanglement of interpenetrating networks only occurs at large deformations and results in fluidization. Yield strains and stresses increase with increasing shear rate or frequency, suggesting a progressive dominance of the timescale associated with shear over that associated with the internal dynamics of the system. (C) 2020 Elsevier Inc. All rights reserved.