The mod, Necromancy 101, allows this. A warning: enemy Necromancers will be able to re-reanimate corpses too.
From its description:
Once the effect fades or it's killed again, [reanimated corpses] will fall to the floor instead of crumbling to ashes. This way you will be able to raise it again.
If you place a garlic on a corpse inventory and someone (you included) cast a raising spell on it, it will, the very moment it's reanimate process has been completed will die and crumble to ashes. This is to avoid enemy necromancers ruining your day by raising corpses over and over again. Besides, that could be a good reason for vampire hunters to use garlic and for common folks to think wrongly a garlic is a valued weapon against vampires (vampires tend to raise each other, so, this could justify histories about a vampire crumbling to ashes for the effect of a garlic.