We create Constitutions for private companies.
This entity will allow your company to have an ABN and remain in the public domain, but the company constitution will be the law the company is bound by, similar to a trust.
A Private Company when registered with an ACN and an ABN and usually registers for GST too.
A company as trustee should not be registered for GST but many are by your favourite accountant or solicitor giving you the pleasure of contracting with the ATO (a (foreign???) private trust).
We are working on deconstructing the ACN and ABN to discover what they really mean and how to undo the links that bind to each one.