On proper E6 with 6 baths you develop b&w picture separately with the First Developer - this you can push or pull as you like or as film specs recommends. Later separately with Color Developer you develop colors to it - this must be stpot on, off the mark or messed chemical will start to create casts. Ie Fuji Provia 400X can be pulled to ASA200 or pushed all the way to ASA1600 and some say even ASA3200 can be acceptible, with just normal slightly increased grain during the FD-process, with nice "spot-on" colors from CD-process. So pushing is allright in proper E6 within film's tolerances.