How do you calculate the CR of this beastie?

Quartz

Hero
How do you calculate the CR of a critter with multiple heads where each head has a seperate spellcasting ability?

Let's invent a Doom Dog, offspring of Cerberus. We'll start with giving it 10 HD and enough other stuff to give it a base CR of 10. We'll then give it three heads: one head is a 10th level sorceror, the second a 10th level cleric, and the third a 10th level druid. All can take independent actions. What's the new CR? My gut feeling is that it's a weak +2. It's essentially three CR10 monsters stuck together. But is there an official way of calculating this?
 

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