While you are correct that it is not possible to customise the process template on Visual Studio Online you do have a few options:
- Kanban Columns - If you want to you can customise the Kanban columns so that you have 'meta states' that you can use. I know that it is not the same but it could get you there.
- Go offline - Currently and for a limited time you can take your VSO account on-premises. The TFS team are holding the version of VSO in parity with TFS 2013 Update 2 so that folks can do this. Be aware of what you loose though. No frequent updates and you have to host your own servers...
Not sure if these options help but they are options...