You need two lots of permissions:
First you will need the permission of the owners corp (because it’s their property) and you will also need the permission of the local council (who will want to see the OC permission).
You will have to get a by-law passed which should pass responsibility for all affected common property to you.
You will have to pay something to the OC. At the VERY LEAST it will be the difference in the value of your property with and without the extension, minus the cost of the work.
You should probably pay more than that to make it worth your neighbours while. They are under no obligation to allow you to do this.
You should cover all legal costs, costs of the by-law etc etc.
You should also offer to apply to NCAT to adjust the Unit Entitlements so that you are paying more and your neighbours are paying a bit less.