I would like is for users to be able to select state based on their country

Is it possible for users to add their own predefined list - just like you have for US states?

What I would like is for users to be able to select state based on their country. I appreciate not being able to provide all states for all countries, but I would like to add in options for Australia and the US, and if neither of these are selected, allow the user to manually input their state (ie. If their country is not one of these two?)

Please try the All States and Cities widget: 

Let us know if you need more help, we will be glad to assist you.