JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://code.jquery.com/jquery-2.1.4.min.js"></script>
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css" rel="stylesheet" type="text/css" />
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/js/bootstrap.min.js"></script> 
 <a data-toggle="modal" href="#myModal" class="btn btn-primary">Abrir</a>
<div class="modal fade" id="myModal">
    <div class="modal-dialog">
        <div class="modal-content">
            <div class="modal-header">
                <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
                	<h4 class="modal-title">Modal 1</h4>
            </div>
            <div class="container"></div>
            <div class="modal-body">Alguma coisa aqui dentro.
              <a data-toggle="modal" href="#myModal2" class="btn btn-primary">Abrir</a>
            </div>
            <div class="modal-footer">
              <a href="#" data-dismiss="modal" class="btn btn-danger">Fechar</a>
	<a href="#" class="btn btn-primary">Outro botão a ser implementado</a>
            </div>
        </div>
    </div>
</div>
<div class="modal fade" id="myModal2">
    <div class="modal-dialog">
        <div class="modal-content">
            <div class="modal-header">
                <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
                	<h4 class="modal-title">Modal 2</h4>
            </div>
            <div class="container"></div>
            <div class="modal-body">Alguma coisa aqui dentro.
              <a data-toggle="modal" href="#myModal3" class="btn btn-primary">Abrir</a>
            </div>
            <div class="modal-footer">
              <a href="#" data-dismiss="modal" class="btn btn-danger">Fechar</a>
            </div>
        </div>
    </div>
</div>
<div class="modal fade" id="myModal3">
    <div class="modal-dialog">
        <div class="modal-content">
            <div class="modal-header">
               ...

JavaScript

$(document).ready(function () {
    $('#abrir').click(function () {
        $('#myModal').modal({
            show: true
        })
    });
        $(document).on('show.bs.modal', '.modal', function (event) {
            var zIndex = 1040 + (10 * $('.modal:visible').length);
            $(this).css('z-index', zIndex);
            setTimeout(function() {
                $('.modal-backdrop').not('.modal-stack').css('z-index', zIndex - 1).addClass('modal-stack');
            }, 0);
        });
});