Despite their wide range of applications, there is a remarkable lack of fundamental understanding about how micelles respond to other components in solution. The colloidal stability of micellar solutions in presence of (homo)polymers is investigated here following a theoretical bottom-up approach. A polymer-mediated micelle-micelle interaction is extracted from changes in the micelle-unimer equilibrium as a function of the inter-micelle distance. The homopolymer-mediated diblock copolymer micelle-micelle interaction is studied both for depletion and adsorption of the homopolymer. The fluffy nature of the solvophilic domain (corona) of the micelle weakens the depletion-induced destabilization. Accumulation of polymers into the corona induces bridging attraction between micelles. In fact, both depletion and adsorption phenomena are regulated by the coronal thickness relative to the size of the added polymer. Penetration of guest compounds into the coronal domain of crew-cut micelles, with a narrower yet denser corona, is less pronounced as for starlike micelles (with a more diffuse corona). Therefore, crew-cut micelles are less sensitive to the effect of added compounds, and hence more suitable for applications in multicomponent systems, such as industrial formulations or biological fluids. The trends observed for the colloidal stability of crew-cut micelles qualitatively match with our experimental observations on aqueous dispersions of polycaprolactone-polyethylene glycol (PCL-PEO) micellar suspensions with added PEO chains.