In an athermal blend of nanoparticles and homopolymer near a hard wall, there is a first order phase transition in which the nanoparticles segregate to the wall and form a densely packed monolayer above a certain nanoparticle density. Previous investigations of this phase transition employed a fluids density functional theory (DFT) at constant packing fraction. Here we report further DFT calculations to probe the robustness of this phase transition. We find that the phase transition also occurs in athermal systems at constant pressure, the more natural experimental condition than constant packing fraction. Adding nanoparticle-polymer attractions increases the nanoparticle transition density, while sufficiently strong attractions suppress the first-order transition entirely. In this case the systems display a continuous transition to a bulk layered state. Adding attractions between the polymers and the wall has a similar effect of delaying and then suppressing the first-order nanoparticle segregation transition, but does not lead to any continuous phase transitions.