Diverter stem broken - unable to remove

Diverter stem broke off, unable to remove last bit through the passage due to some corrosion (I think) on the stem remnant. The stem is a Sayco. Any hints? Is it possible to simply plug the valve and install a spout w/ a diverter?

Thanks

diverter

I would have to see what you did, but it appears that you may have tried to remove it improperly. Sayco stems are notorious for breaking off it you are just trying to unscrew it after removing the packing nut. Other valves would just "jam" until you removed them properly.