You can't do this in html.
You can have a drop down box - it is in html a <select> control, and then separately have an input text box <input type="text".. where a user can enter data if it is not in the list.
OR....
On a site I made, there was a drop down ( in html a <select> control), and then I had a button the opened a popup window where the user could click the button, open the popup window and there was a form to enter the new value....
Then I had javascript code to take what they entered on the popup window and add it to the drop down or select control.
There's a couple of alternative choices... for you. Sorry