Change Enslave Demon to being demonology only.
Make 'Enslave Demon' like the hunter ability to get your own pet.
Make demons caught with 'enslave demon' more powerful than demons you can normally summon with other classes. The enslaved demons can be stored like hunter pets and can be used whenever you want.
Remove the CD for summoning added pets. Leave them up until they officially 'die.'
Make Demonic Empowerment into a passive.
make their rotation be spells that deal DPS to the target but also buffs up existing pets as well. (for example... Shadowbolt deals X damage. Hastes your pets by 20% for 3 seconds)
Provide a clear life pool and how many pets are active on the side.
Most of their dps will come from their demons. You get the feeling that you command hordes of demons and you can get "special demons" that no other class can get by 'enslaving' them.
Just my thoughts.