Puppies!

Puppies! is a perk added to Fallout 3 with the Broken Steel add-on.

With this perk, one of Dogmeat's puppy offspring will take his place every time he dies, and that pup can be added as a companion, either by finding Dogmeat's pup at the location of his death or by waiting a day or two and returning to Vault 101's entrance. Dogmeat's puppy is much tougher than the original Dogmeat, and will level with the player in terms of damage done and health.

Despite the name, this perk only allows you to get one of Dogmeat's puppies at a time. If it dies, it will be replaced by a new puppy.

This perk still works if Dogmeat died pre-Broken Steel.

Bugs
With this you may be able to get all of the followers. See Fallout 3 exploits for more details.

Welpen! Szczenięta! Щеночки!