The closest I can find in RAW rules is a Vampire Spawn (which is, more basically, a weaker vampire)

Create Spawn (Su) A humanoid or monstrous humanoid slain by a vampire’s energy drain rises as a vampire spawn 1d4 days after burial.

If the vampire instead drains the victim’s Constitution to 0 or lower, the victim returns as a spawn if it had 4 or less HD and as a vampire if it had 5 or more HD. In either case, the new vampire or spawn is under the command of the vampire that created it and remains enslaved until its master’s destruction. At any given time a vampire may have enslaved spawn totaling no more than twice its own Hit Dice; any spawn it creates that would exceed this limit are created as free-willed vampires or vampire spawn. A vampire that is enslaved may create and enslave spawn of its own, so a master vampire can control a number of lesser vampires in this fashion. A vampire may voluntarily free an enslaved spawn in order to enslave a new spawn, but once freed, a vampire or vampire spawn cannot be enslaved again.

But the beauty of DnD is RULE 0, the DM makes the rules.

If you can create a fair/balanced system, with enough flavor, your DM could allow it.

The closest I can find in RAW rules is a Vampire Spawn (which is, more basically, a weaker vampire)

Create Spawn (Su) A humanoid or monstrous humanoid slain by a vampire’s energy drain rises as a vampire spawn 1d4 days after burial.

If the vampire instead drains the victim’s Constitution to 0 or lower, the victim returns as a spawn if it had 4 or less HD and as a vampire if it had 5 or more HD. In either case, the new vampire or spawn is under the command of the vampire that created it and remains enslaved until its master’s destruction. At any given time a vampire may have enslaved spawn totaling no more than twice its own Hit Dice; any spawn it creates that would exceed this limit are created as free-willed vampires or vampire spawn. A vampire that is enslaved may create and enslave spawn of its own, so a master vampire can control a number of lesser vampires in this fashion. A vampire may voluntarily free an enslaved spawn in order to enslave a new spawn, but once freed, a vampire or vampire spawn cannot be enslaved again.

But the beauty of DnD is RULE 0: the DM makes the rules.

If you can create a fair/balanced system, with enough flavor, your DM could allow it.