Funny you should ask

I work a 9-5, own The Virtual Office Goddess (VA bookkeeping business), own TVE Magazine (ezine for virtual entrepreneurs) and am a co-owner of the Virtual Academy of Education (online skills training for VAs). So, yes! It is VERY possible to own/operate multiple businesses.
The primary skill required to handle multiple businesses is time management. I have specific set schedules for which business venture I am working on at any given time. You will find quite a few VAs on VAF that work a 9-5 as well as growing their own VA businesses and you may find the threads devoted to that process help you to plan and organize your own multiple ventures.