How to place a standalone fixed-Div layered between(z-index) a fixed Parent and Absolute-Child division?

I have two fixed components:

Parent with its absolute positioned Child
Between

I have used z-index for all three elements but those aren't a must. I cannot remove the z-index:666 of the parent nor can I remove its position:fixed as it'll mess-up the site layout...

rest z-indices can be changed... the goal is to bring the Between element between Parent and Child elements...

Here's my Code:

* {
  color: white;
  width: 40vw;
  height: 30vh;
  text-align: right;
  padding: 1rem
}

#parent {
  position: fixed;
  top: 30vh;
  height: 50vh;
  background: red;
  left: 0;
  right: 0;
  width: auto;
  z-index: 666;
}

#child {
  position: absolute;
  top: 5vh;
  background: orange;
  left: 30vw;
  z-index: 888;
}

#between {
  position: fixed;
  top: 40vh;
  background: green;
  left: 10vw;
  z-index: 777;
}

<div id="parent">
  Parent
  <div id="child">
    Child
  </div>
</div>
<div id="between">
  Between
</div>

Solution

An idea of solution that works but will break the position:fixed. It uses 3D transformation tricks

body * {
  color: white;
  width: 40vw;
  height: 30vh;
  text-align: right;
  padding: 1rem
}

#parent {
  position: fixed;
  top: 30vh;
  height: 50vh;
  background: red;
  left: 0;
  right: 0;
  width: auto;
  z-index: 666;
}

#child {
  position: absolute;
  top: 5vh;
  background: orange;
  left: 30vw;
  z-index: 888;
  transform:translateZ(2px); /* here */
}

#between {
  position: fixed;
  top: 40vh;
  background: green;
  left: 10vw;
  z-index: 777;
}

html {
  transform-style:preserve-3d; /* here */
}

<div id="parent">
  Parent
  <div id="child">
    Child
  </div>
</div>
<div id="between">
  Between
</div>