Echo planar imaging (EPI) is a widely used rapid MRI technique to image dynamic neurological functionally, but can suffer from Nyquist ghosts and distortions due to magnetic field inhomogeneity. Distortion effects can be reduced by parallel MR imaging (pMRI), via a reduced echo train length, and/or methods that measure and estimate magnetic field distortions using multiple TEs. Recent Nyquist ghost correction methods can also improve self-referenced pMRI image reconstruction quality. Here, we present a combination of these improvements in a framework for continuous echo planar imaging. Through a combination of shifted variable density EPI trajectories and alternating echo spacings, our approach can remove Nyquist ghosts, apply pMRI reconstruction, and correct off-resonant distortions with no need for additional reference data. Results from accelerated in-vivo data are presented.