Yes, you're allowed to start a business on an open work visa, but you can't run it after that visa comes to an end.
If by any chance you were to have a partner - as in, life partner - who was a NZ citizen or resident, that person could sponsor you for a partner-sponsored temporary work visa
http://www.immigration.govt.nz/migra...milystream.htm, which is an open visa also, and that would allow you to run your business. A partner can sponsor you for Residence in due course, too, after you have lived together for 12 months.