We present the use of n - phase cylindrical vector beams in optical trapping. The vector beams are created via a Mach- Zehnder interferometer equipped with tunable phase plates, and the "n" prefix indicates the relative phase between the Hermite-Gaussian modes comprising the output beam. The optical trapping efficiency is measured via the Stokes drag force method for radial and azimuthal vector beams with n = 0 and π, giving a total of 4 unique input beams. Additionally, their trapping efficiencies are compared with that of a standard Gaussian input beam of equal input power. We find that the axial trapping efficiency can be optimized by increasing the amount of longitudinal (z) polarization at the focal plane of the trapping objective. Further, the lateral trapping efficiency is determined by the focal spot diameter, as expected, and can be similarly tuned by varying the relative phase between the vector beams' eigenmodes. The results suggest that cylindrical vector beams may be tuned such that both axial and lateral trapping efficiencies can be maximized.