For what it’s worth, the Blender developers are aware of the desire to have this… it’d be especially useful for those of us rendering on farms or on machines with two or more GPUs. But as already noted, it’s a non-trivial task.
The difficulty, as I understand it (I’m sure someone will correct me if I’m wrong) is that Eevee is a realtime render engine that depends on OpenGL. If you’re rendering with OpenGL, it requires something called a “context” for drawing… and that context requires a screen to draw upon. Since typically only one GPU is ever used for drawing to the screen, that’s the only one that’s available for OpenGL rendering… and, by extension, that’s the only GPU available to Eevee.
There might be some ways to work around this, but from what I can tell, that’s exactly what they are: workarounds… and sometimes pretty kludgey ones at that.
I have a hope that this can be handled in the future… but I wouldn’t count on seeing it anywhere in the near term.