Beast Keeper
"Lets you cage your beasts, 3 at a time, allowing you to change your attacking Beast and protect the rest from attack."
To unlock all beasts you will need the Beast Keeper, since you can only have one beast in the Beast Cave at the time, you will need to have a safe place for the other beasts.
Beasts in the Beast Keeper are safe from damage, even if the Beast Keeper is destroyed your beasts will be safe. Also the beast are resting in the Beast Keeper and can't be trained while in the Beast Keeper. The beasts do not lose levels, progress or bonuses if they are in the Beast Keeper. This is a must have building if you want to have and train all the available beasts.