The closest Thing in WordPress would be a custom meta box with repeatable fields.
So to do that you would need create a a metabox using add_meta_box and if you look at this link you will also see an example of saving the custom fields in your meta box.
here is an example on a related question or if you want a much better option is to use a ready made class which will let you do just that with a few OOP settings.
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