Presumably you will be using a C41 kit, which is fine. I would suggest that after you have cross processed any E6 in a C41 bath, then further usage of that bath using C41 films could be compromised by possibly giving you slightly skewed C41 negatives.
Back in the day when we were running huge Dip N Dunk C41 baths, we would keep any cross processed E6 until the end of the day. We then ran test strips and measured the amount of off balance the C41 bath was at after running E6 films through it. We then placed the suggested correction into the bath, with the hope it would be reasonably correct in the morning; which it usually was.
Whatever you do, if you are precise, then in the future anything you end up with that you like, should be reasonably repeatable. The less precise one is the less repeatable you may find things.
C41 is about the shortest process around, so you need to be on the ball for 3'15" then put a stop bath in (which is not in the C41 process but is not a problem to add), then you relax and do your Blix or bleach and fix baths with reasonable ease.
Mick.