For characters with class levels, CR is Level -1 (CR½ for level one characters). I'm not sure what RAW says about adding class levels to creatures, but I'm gonna say for my games that it will increase the CR by 1 per class level added. I can't see giving a Dire Ape an extra HD, the ability to Rage and access to Martial Weapons, Armor and Shields without also bumping the CR, for example (not a good one, as it's still animal intelligence).