Palm stump? I'm wondering why its a stump, and you don't say what kind of 'palm' it is. If it's Cordyline, and the shoots are coming off the trunk stump, but not from the ground at the base, these will not grow on separately - shoots from the soil at the base can be, provided you can get a good piece of root with each one - but this should not be done now, best in Spring.

It does sound very much like a Cordyline...