The polymer-induced forces between colloidal particles in a semidilute or concentrated polymer solution are considered theoretically. This study is focussed on the case of partially adsorbing colloidal surfaces involving some attractive centers able to trap polymer segments. In the presence of free polymers the particles are covered by self-assembled fluffy layers whose structure is elucidated. It is shown that the free-polymer-induced interaction between the particles is repulsive at distances exceeding the polymer correlation length, and that this depletion repulsion can be strongly enhanced due to the presence of fluffy layers. This enhanced depletion stabilization mechanism (which works in tandem with a more short-range steric repulsion of fluffy layers) can serve on its own to stabilize colloidal dispersions. More generally, we identify three main polymer-induced interaction mechanisms: depletion repulsion, depletion attraction, and steric repulsion. Their competition is analyzed both numerically and analytically based on an asymptotically rigorous mean-field theory. It is shown that colloid stabilization can be achieved by simply increasing the molecular weight of polymer additives, or by changing their concentration.