A compressible regular solution free energy model for describing the phase behavior of weakly interacting binary blends comprising nonrigid polymer nanoparticles and linear-polymer chains (i.e., all-polymer nanocomposites) has been developed by incorporating specific nanoparticle-nanoparticle and nanoparticle-polymer contributions into the original free volume theory for binary polymer blends of Ruzette et al. [J. Chem. Phys. 114, 8205 (2001)]. The extended model allows predicting phase behavior for weakly interacting polymer-nanoparticle/linear-polymer nanocomposites using only pure component properties (nanoparticle and polymer sizes, mass densities, coefficients of thermal expansion, and solubility parameters). The effect of polymer and nanoparticle size, as well as those arising from nanoparticle rigidity, exchange interaction energy and composition on the phase behavior of all-polymer nanocomposites have been systematically investigated. A rich variety of phase diagrams (including upper critical solution temperature-type, lower critical solution temperature-type, and hour-glass shape) are illustrated. Predicted phase diagrams for nonrigid poly(styrene)-nanoparticle (PS-np)/linear-poly(styrene) (l-PS), and branched poly(ethylene)-nanoparticle (PE-np)/l-PS nanocomposites were in excellent agreement with available experimental data.