CSS drop down menu, Adding another <ul>

Question

I have a drop down menu made with css and at the moment it has 5 li that are visable. When you hover over one of the li it highlights and then the drop down effect happens and the next ul shows underneath. So basically you have a first set of options to choose from and then when you hover over the first set of options you get a second set of options. What I would like to do is make a third set of options appear when you hover over the second set of options and make this third set of options appear to the right of the second options.

a link to exactly what i would like to do: http://cssmenumaker.com/menu/opera-drop-down-menu

Here is my html. Note the descriptions of the li are not final i will change what i want the links to say later.

<li><a href="#">Home</a>
<ul class="subforums">
<li><a href="#">Elite's</a></li>
<li><a href="#">Newbs</a></li>
<li><a href="#">Subscribers</a></li>
</ul>
</li>
<li><a href="#">Samples</a>
<ul class="subsites">
<li><a href="#">Architecture</a></li>
<li><a href="#">Furniture</a></li>
</ul>
</li>
<li><a href="#">Workshop</a>
<ul class="subcontactus">
<li><a href="#">By Phone</a></li>
<li><a href="#">By e-mail</a></li>
<li><a href="#">By Text</a></li>
</ul>
</li>
<li><a href="#">About</a>
<ul class="subabout">
<li><a href="#">The Team</a></li>
<li><a href="#">Our Story</a></li>
<li><a href="#">Our Goal</a></li>
</ul>
</li>
<li><a href="#">Contact Us</a>
<ul class="subsignup">
<li><a href="#">Find Out More</a></li>
<li><a href="#">Costs</a></li>
<li><a href="#">Paying Methods</a></li>
</ul>
</li>
</ul>

` note: there is a ul opening tag before all of the html that i have just posted but it wouldn't let me have it on here for some reason.

and the css:

navmenu is the id for the opening ul of the whole drop down menu `#navmenu, #navmenu ul{ list-style-type: none; }

#navmenu li{
width: 125px;
text-align: center;
position: relative;
float: left;
margin-right: 4px;
}
#navmenu a{
text-decoration: none;
display: block;
width: 125px;
height: 25px;
line-height: 25px;
background-color: #00cff0;
border: 1px solid #ccc;
border-radius: 5px;
color: white;
}
#navmenu li:hover > a{
background-color: #00d3f5;
}
#navmenu li:hover a:hover{
font-size: 105%;
}
#navmenu ul{
display: block;
position:absolute;
top: 26px;
left: 0;
visibility: hidden;
margin: 0;
padding: 0;
}
#navmenu li:hover ul{
visibility: visible;
}
#navmenu{
margin: auto;
width: 700px;
}`#navmenu, #navmenu ul{
list-style-type: none;
}
#navmenu li{
width: 125px;
text-align: center;
position: relative;
float: left;
margin-right: 4px;
}
#navmenu a{
text-decoration: none;
display: block;
width: 125px;
height: 25px;
line-height: 25px;
background-color: #00cff0;
border: 1px solid #ccc;
border-radius: 5px;
color: white;
}
#navmenu li:hover > a{
background-color: #00d3f5;
}
#navmenu li:hover a:hover{
font-size: 105%;
}
#navmenu ul{
display: block;
position:absolute;
top: 26px;
left: 0;
visibility: hidden;
margin: 0;
padding: 0;
}
#navmenu li:hover ul{
visibility: visible;
}
#navmenu{
margin: auto;
width: 700px;
}

I hope you can understand this and help me out. I have tried to be as clear as possible thankyou for reading. :)

Answer 1

Working Demo Here

you need to add these calsses to your css:

ul#navmenu li ul li ul {
    list-style-type: none;
    position: absolute;
    display: none;
    left: 0;
    margin: -26px 0 0 127px;
    padding: 0;
}
ul#navmenu li ul li:hover ul {
    display: block;
}

you can see your code on JSFiddle

Answer 2

If means anything to you I made this FIDDLE couple of days ago for similar question

<div id="menu">
  <ul>
    <li><a href="index.php">Home</a></li>
    <li><a href="#">Link 2</a>
      <ul class="submenu">
        <li><a href="#">Link 2.1</a></li>
        <li><a href="#">Link 2.2</a></li>
        <li><a href="#">Link 2.3</a></li>
        <li><a href="#">Link 2.4</a></li>
        <li><a href="#">Link 2.5</a></li>
      </ul>
    </li>
    <li><a href="#">Link 3</a>
      <ul class="submenu">
        <li><a href="#">Link 3.1</a></li>
        <li><a href="#">Link 3.2</a></li>
        <li><a href="#">Link 3.3</a></li>
        <li><a href="#">Link 3.4</a></li>
        <li><a href="#">Link 3.5</a>
          <ul class="sub-submenu">
            <li><a href="#">Link 3.5.1</a></li>
            <li><a href="#">Link 3.5.2</a></li>
            <li><a href="#">Link 3.5.3</a></li>
            <li><a href="#">Link 3.5.4</a></li>
            <li><a href="#">Link 3.5.5</a></li>
          </ul> 
        </li>
      </ul>
    </li>
    <li><a href="#">Link 4</a></li>
    <li><a href="#">Link 5</a></li>
  </ul>
</div>

---

#menu {
  background: #333;
  width: 960px;
  margin: 0 auto;
  height: 30px;
}
#menu ul {
  list-style: none;
}
#menu ul li {
  float: left;
}
#menu ul li a {
  display: block;
  height: 25px;
  padding: 5px 10px 0 10px;
  font-family: Verdana;
  font-size: 16px;
  letter-spacing: 1px;
  text-decoration: none;
  color: #fff;
  text-shadow: 1px 1px 0 #252525;
  transition: all 0.2s linear;
}
#menu ul li a:hover {
  background: #555;
  color: #00aeff;
}
#menu ul li .submenu {
  background: #333;
  position: absolute;
  display: none;
  top: 46px;
  margin-left: 0;
  padding: 0;
  width: 150px;    
}
#menu ul li:hover .submenu {
  display: block;
}
#menu ul li .submenu li {
  margin-bottom: 5px;
  width: 100%;
}
#menu ul li .submenu li .sub-submenu {
  background: #333;
  position: absolute;
  display: none;
  left: 0;
  margin: -30px 0 0 150px;
  padding: 0;
  width: 150px;    
}
#menu ul li .submenu li:hover .sub-submenu {
  display: block;
}

Answer 3

I think I have what you are after.

3 level menu.

Codepen Example