How to stack/overlap more than 2 icons in Font Awesome?

I had a similar issue and solved using some custom CSS.

.icon-stack {
  position: relative;
  display: inline-block;
  width: 2em;
  height: 2em;
  line-height: 2em;
  vertical-align: middle;
}
.icon-stack-1x,
.icon-stack-2x,
.icon-stack-3x {
  position: absolute;
  left: 0;
  width: 100%;
  text-align: center;
}
.icon-stack-1x {
  line-height: inherit;
}
.icon-stack-2x {
  font-size: 1.5em;
}
.icon-stack-3x {
  font-size: 2em;
}

Markup is therefore:

<span class="icon-stack fa-3x">
   <i class="fa fa-{{whatever icon 3}} icon-stack-3x"></i>
   <i class="fa fa-{{whatever icon 2}} icon-stack-2x"></i>
   <i class="fa fa-{{whatever icon 1}} icon-stack-1x"></i>
</span>

I decided rather than override fa-stack I'd duplicate so I can still use the original CSS if required.

You can obviously play around with the font size, line height etc to suit your own requirements.

Finally, a new feature from Font-Awesome was released and now you can stack more than 2 icons:

See the following link: https://fontawesome.com/how-to-use/on-the-web/styling/layering