Multiple dock icons for single Electron app?

Question

My Electron app has two modes, let's call them A and B.*

When switching between the two modes, I'm creating a new BrowserWindow and changing the dock icon (see "What I've Tried" below).

Is there a way to make it so that when a user right-clicks > "Keep in Dock" on MacOS in Mode A it creates a distinct docked app icon that launches the app into mode A, and vice versa for mode B?

I.e. is it possible to have multiple docked icons for a single Electron app?

---

*: The modes A and B essentially boots the same React app, where A is a stripped-down version of the app. Some users prefer to only use the stripped down version, which is why I want to enable docking separate versions of the app. And I don't want to bundle A as a separate app since the user needs to be able to switch between the two modes inside the app's UI.

What I've tried

let windowA;
let windowB;

const bootInModeA = () => {
  windowA = new BrowserWindow({
    ...,
    icon: 'iconA.png',
  })

  // Change dock icon.
  const realmImage = nativeImage.createFromPath(getAssetPath('iconA.png'));
  app.dock.setIcon(realmImage);
};

const bootInModeY = () => {
  // Vice versa.
};

const bootApp = () => {
  // Create a throwaway window so the main process remains open.
  const throwawayWindow = new BrowserWindow({
    show: false,
  });

  if (isModeA) {
    windowB.close()
    bootInModeA();
  } else {
    windowA.close()
    bootInModeB();
  }

  throwawayWindow.close();
}

The problem is that right-click > "Keep in Dock" pins the same app icon and provides me with no information about what version of the app they want to keep pinned.

I could create a custom "Keep in Dock" MenuItem that stores the last mode with electron-store, however this doesn't allow two different dock icons.

Any pointers appreciated.