Triple-diffusive convection for nanofluids in which differences in density are derived because of triple diffusion process, i.e., with three diffusing components: nanoparticles, solute, and heat, using more realistic two temperature model with separate thermal energy equations for the two phases of the considered nanofluid has been investigated by making use of the method of superposition and one term Galerkin technique. A complex system with local thermal non-equilibrium (LTNE) effects along with the Brownian motions and thermophoresis to account for nanoparticles has been considered. The problem is solved for top-heavy arrangement of nanoparticles leading to stationary mode of convection and numerical computations are carried out by using Mathematica software. An additional solute concentration equation supplements the conservation equations due to the existence of solute, which introduces two additional nondimensional parameters, whereas three additional parameters came into existence due to the consideration of LTNE effects. The critical Rayleigh number remains constant for smaller values of interphase heat transfer parameter, whereas it diminishes for the intermediate range and approaches to constant value for higher ranges of the parameters. What all this means is that only the intermediate range of Nield parameter shows stabilizing/destabilizing effects. Interestingly, the additional parameters Lewis number and solute Rayleigh number enhance the effect of destabilization of considered nanofluid layer.