This work presents a rate-dependent constitutive model for porous single crystals with arbitrary number of slip systems and orientations. The single crystal comprises cylindrical voids with elliptical cross-section at arbitrary orientations and is subjected to general plane-strain loadings. The proposed model, called modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous single crystal material to estimate the response of the nonlinear porous single crystal. The MVAR model is validated by periodic finite element simulations for a large number of parameters including general in-plane crystal anisotropy, general in-plane void shapes and orientations, various creep exponents (i.e., nonlinearity) and general plane strain loading conditions. The MVAR model, which at the present state involves no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in this work. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids.