Based on the contents of this thread, I think its a safe bet the process doesn't exist yet. Jon Hall will most certainly share the process with us as soon as they have something ready.
It's all in development currently. VMware are working on vSphere versions of both the Enterprise Administration and Design exams - no release dates have been announced. They are now accepting vSphere-centric designs for the Design Defence, but that's for those who have done VCP3 + Enterprise3 + Design3 - so you will still end up as a VCDX3 even if you were to submit and defend a vSphere design.
It's definitely going to be the exam versions that will define the VCDX version - so until there are confirmed release dates for the v4 Enterprise Administration and Design exams, I doubt we'll hear too much announced officially. I'm interested in the "upgrade" process for those that are part way through (like me!) and those lucky few that have already got VCDX3.....