The nucleus-nucleus total reaction cross section at 30-1000 MeV/n is studied, using a modified Coulomb Glauber model, which includes combined effects due to phase variation, higher momentum transfer components, Pauli blocking, and a finite range. The total reaction cross sections of the reactions: 12C + 12C, 4He + 16O, 20Ne + 12C, 8Li + 9Be, 8Li + 12C and 8Li + 27Al using different densities of the harmonic oscillator single-particle wave function (SDHO) are calculated and compared with the available experimental data and previous calculations. Using a simulated search program, the phase variation γ_NN parameter is treated as a free parameter to fit the experimental data of the reaction cross section R. A good agreement with the experimental data is obtained. The relationship between the phase variation and finite range parameters as a function of incident energy is discussed. We investigated combined effects on p - 16O reaction cross sections and compared with the available experimental data and previous calculations.