Hi,
From my understanding this can be done easily. I would process each stack of images to the point before doing a StarAlignment. ie, Calibrated, CosmeticCorrection, Debayer (if required), SubframeSelector. Your image stacks are now "clean". Now use StarAlignment to combine all clean image stacks. Finish with maybe LocalNormalization(optional) and finalize with ImageIntegration and DrizzleIntegration (optional).
space is not black
John