Juet to clarify: A mythic eternal is an eternal item like Fabled Blade and Unreal Hood. They already have 4 sockets and when you fill them with a mythic, it has the mythic.
For eg, if you plan to put say discordance on your unreal hood hat, the mythic would be there but the Eternal will still be green, still have the same Eternal Unreal Hood name but the difference is that the item will now have the discordance mythic and some slots to fill.
You can add some epic affixes using Topaz which are most likely to be perfect to the now mythic eternal to enhance the item. I don't know about afterwards but I believe the epic affixes added onto the Eternal Unreal Hood mythic item cannot be removed. If that's the case, lots of trial and error for what you want I guess.
Hope this helps you understand how it all works .