The authors develop systematic 1/ rho expansions for the rho -spin interaction spin-glass model in a transverse field. This model can be solved using the static approximation (SA), which is expected to be valid in the limit rho to infinity . For large, but finite rho , corrections to SA can be obtained, and the non-trivial time dependence of the imaginary time correlation function for quantum spins calculated. These corrections qualitatively change the low temperature behaviour for large rho . In particular the corrections to the SA result in the entropy vanishing exponentially as the temperature tends to zero. They compute the finite rho changes in the phase diagram, and discuss the emergence of a new critical point ending the transition line separating the two paramagnetic phases.