<?php
     session_start();
     if($_POST['btnOne'])
       $_SESSION['ShowSecond'] = true;
     if($_POST['btnTwo'])
       $_SESSION['ShowThird'] = true;
    ?>
    <form name="formOne">
    ...
    <input type="submit" name="bntOne" value="One">
    </form>
    <?php if(isset($_SESSION['ShowSecond'])) { ?>
    <form name="formTwo">
    ...
    <input type="submit" name="bntTwo" value="Two">
    </form>
    <?php }
    if(isset($_SESSION['ShowThird']))
    {
    ?>
    <form name="formThree">
    ...
    <input type="submit" name="btnThree" value="Three">
    </form>
    <?php } ?>
    ?>

<form name="myform" method="post" action="">
  <?php if(!isset($_POST['firstname']))
         {?>
            First Name?
           <input type="text" name="firstname" value="">
  <?php  }
        elseif(!isset($_POST['middlename']))
         {?>
      <input type="hidden" name="firstname" value="<?php echo $_POST['firstname'] ?>">
            First Name? <?php echo $_POST['firstname'] ?><br>
            Middle Name?
            <input type="text" name="middlename" value="">

  <?php  }
        elseif(!isset($_POST['lastname']))
         {?>
      <input type="hidden" name="firstname" value="<?php echo $_POST['firstname'] ?>">
      <input type="hidden" name="middlename" value="<?php echo $_POST['middlename'] ?>">
          First Name? <?php echo $_POST['firstname'] ?><br>
          Middle Name? <?php echo $_POST['middlename'] ?><br>
          Last Name?
         <input type="text" name="lastname" value="">
  <?php  }else{ ?>
      <input type="hidden" name="firstname" value="<?php echo $_POST['firstname'] ?>">
      <input type="hidden" name="middlename" value="<?php echo $_POST['middlename'] ?>">
      <input type="hidden" name="lastname" value="<?php echo $_POST['lastname'] ?>">
          First Name? <?php echo $_POST['firstname'] ?><br>
          Middle Name? <?php echo $_POST['middlename'] ?><br>
          Last Name? <?php echo $_POST['lastname'] ?><br>

  <?php  } ?>

         <input type="submit" name="submitbtn" value="Submit">
        </form>