JSFiddle - React, Tailwind, and code Playground

HTML

<input type="button" id="showMore" value="Show More">
<p class="mult_entries select">
    <select class="filter">
      <option value="dogs">dogs</option>
      <option value="cats">cats</option>
      <option value="chickens">chickens</option>
      <option value="pigs">pigs</option>
    </select>
</p>
<p class="mult_entries select">
    <select class="filter">
      <option value="dogs">dogs</option>
      <option value="cats">cats</option>
      <option value="chickens">chickens</option>
      <option value="pigs">pigs</option>
    </select>
</p>
<p class="mult_entries select">
    <select class="filter">
      <option value="dogs">dogs</option>
      <option value="cats">cats</option>
      <option value="chickens">chickens</option>
      <option value="pigs">pigs</option>
    </select>
</p>
<p class="mult_entries select">
    <select class="filter">
      <option value="dogs">dogs</option>
      <option value="cats">cats</option>
      <option value="chickens">chickens</option>
      <option value="pigs">pigs</option>
    </select>
</p>

JavaScript

$("p.mult_entries select:gt(0)").hide();
$("#showMore").click(function(){
    $(".mult_entries select:hidden:first").fadeIn("slow");
});
$(".filter").change(function(){
    var val = $(this).val();
    $(".filter").not(this).children().each(function(){
        if ($(this).val() == val) $(this).attr('disabled','disabled');
    });
})