Good afternoon Sergio, I could not understand 100% what you are trying to do, but an idea would be to use a button for the user to click if he does not find his option, which would show an input field, follow an example:
HTML
<select name="something" id="">
<option value="a">a</option>
<option value="b">b</option>
</select>
<button>Não achei a opção</button>
<input type="text" placeholder="Digite aqui" />
CSS
input {
display: none;
}
Javascript
$('button').click(function() {
$('select').fadeOut();
$('input').fadeIn();
});
And here's where you want to see live: link
I hope to have helped, it's an option, there are sure to be lots of ideas.