Recently, multi-contrast EPI approaches have been proposed for a fast screening brain protocol. With EPI-encoding, multiple contrasts can be acquired quickly for robust, quantitative mapping as well as creation of synthetic weighted images. Here, a spatiotemporal subspace reconstruction is developed to jointly reconstruct multi-contrast multishot-EPI data from a multi-inversion Spin and Gradient echo EPI (MI-SAGE-EPI) acquisition. An approach to estimate and incorporate shot-to-shot phase corruption into the reconstruction was also developed. This navigation-free subspace reconstruction achieves good reconstruction for MI-SAGE-EPI at a high EPI-acceleration, thus enabling a rapid quantitative protocol at high in-plane resolution with minimal distortion and blurring.