Handle field repetition with Settings API

Hi,

I read a lot of stuff about Settings API, but I can’t see how to handle this kind of functionnality :

I would like to display multiple options (eg: First Name, Last Name), and to be able to clone theses fields via a button (eg “Add a row”), letting the user make an other entry with the same fields (like repeater field in Advanced Custom Fields plugin).

Last but not leat, if possible, saving all this stuff in a single serialized option would be great.

Any ideas ?
Thanks.