The only way I know is to use it with HTML and CSS, like this:

In your HTML

<div class="wrappingImage">
  <img class="overlappingImage" src="body.png">
  <img class="overlappingImage" src="eyes.png">
  <img class="overlappingImage" src="mouth.png">
</div>

In your CSS

.overlappingImage {
  position: absolut:
  top: 0;
  left: 0;
}

.wrappingImage {
  position: relative;
}

Than you can add a value (like this: <img value="1">) to your images and place them based on this value in your template after clicking a button - so let body = 0, eyes = 1 and mouth = 1.

Hopefully it helps you out!

You can combine the images using node.js packages merge-images and canvas.

const mergeImages = require('merge-images');
const { Canvas, Image } = require('canvas');
const fs = require('fs');

const run = async () => {
    const outputBase64 = await mergeImages(['./body.png', './eyes.png', './mouth.png'], {
        Canvas: Canvas,
        Image: Image
    });

    fs.writeFileSync(
        './output.png',
        outputBase64.replace(/^data:image\/png;base64,/, ''), // remove the base64 prefix
        {'encoding': 'base64'}
    );
}

run();

Input images:

Output image: