How to add another option to a select type field starting from another field automatically?

I created a doctype in which one of the fields is of type select. Now I would like to create a button to automatically add other options to the options of the existing select type field and these new options can be selected afterwards.

That sounds pretty complex as you’ll need to edit the doctype via the API.

Can you change the select field to a child table? It would be much easier to add a button
to add a record to a child table.