Group neuroimaging studies of the cerebral cortex benefit from accurate, surface-based, cross-subject alignment for investigating brain architecture, function and connectivity. There is an increasing amount of high quality data available. However, establishing how different modalities correlate across groups remains an open research question. One reason for this is that the current methods for registration, based on cortical folding, provide sub-optimal alignment of some functional subregions of the brain. A more flexible framework is needed that will allow robust alignment of multiple modalities. We adapt the Fast Primal-Dual (Fast-PD) approach for discrete Markov Random Field (MRF) optimisation to spherical registration by reframing the deformation labels as a discrete set of rotations and propose a novel regularisation term, derived from the geodesic distance between rotation matrices. This formulation allows significant flexibility in the choice of similarity metric. To this end we propose a new multivariate cost function based on the discretisation of a graph-based mutual information measure. Results are presented for alignment driven by scalar metrics of curvature and myelination, and multivariate features derived from functional task performance. These experiments demonstrate the potential of this approach for improving the integration of complementary brain data sets in the future.