We present version 2 of the radiation transfer module SPRAI (Simplex Photon Radiation in the AREPO Implementation). SPRAI is a novel method for solving the equations of transfer on an unstructured mesh using a variant of the short characteristics approach. It has several advantages compared to other approaches: its computational cost is independent of the number of radiation sources (unlike typical ray-tracing methods) and it is less diffusive than moment-based methods. Version 1 of SPRAI has already been shown to do an excellent job of modelling the growth of R-type ionization fronts in low-density gas. However, it does not perform so well with D-type fronts in denser gas unless run with a small time-step. Version 2 of the code addresses this weakness in the algorithm, allowing us to dramatically improve its performance in dense gas. Version 2 of SPRAI also includes two important updates to the microphysics treated in the code: a revised multifrequency framework that allows us to model helium photoionization, and a treatment of the effects of radiation pressure. In this paper, we describe these enhancements to SPRAI and also present several tests of the code.