Yes, it is theoretically possible. This is because an NPC (Non-Profit Company) is not automatically exempt from tax — tax exemption requires a separate application to SARS and is not guaranteed.
If you are converting from a Pty (Proprietary Limited) to an NPC, you will also need a minimum of three directors.
We recommend that you first contact our office and speak to one of our consultants, as it may be more practical to close the existing entity and register a new one instead.