Higgs multiplet in the vector-spinor representations of SO(10), i.e., the 144+ multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry SU(3)_C × SU(2)_L × U(1)_Y and a recent analysis has used such vector-spinors for building a new class of SO(10) grand unification models. Here we discuss the techniques for the computation of several classes of vector-spinor couplings using the recent result on the SO(2N) vertex expansion. The computations include the cubic couplings of the vector-spinors with SO(10) tensors, quartic self-couplings of the vector-spinors, and couplings of the vector-spinors with spinor representations of SO(10). The last set include couplings of vector-spinors with the 16-plets of quarks and lepton and with the 16 and of Higgs. These couplings provide a tool for further development of the SO(10) grand unification using vector-spinor representations. These include study of quark-lepton masses, analysis of dimension five operators including baryon and lepton number violating operators, and study of neutrino masses and mixings. Illustrative examples are given for their computation using a sample of vector-spinor couplings. The vector-spinor couplings arise in a wide class of models when one considers higher dimensional operators such as those that arise in the analysis of Planck scale physics and thus the techniques as well as the explicit couplings discussed here should find a wider application. .