You want to know how your pets will behave all together, the coexistence will be the right one, but all that depends on you mainly.
You as the human household manager you should examine the behavior of each of your pets, if your dogs are aggressive or your cats are dominant, or your canary sings a lot.
You should keep in mind the temperament of each of your pets when you buy them in a pet shop, so that they can cope in the best possible way and keep in mind the caring for an iguana domestic.
An example, if your iguana is showing symptoms of aggressiveness either because she’s in heat, because she’s stressed out or because open your mouth and growls, that means you should keep her in the terrarium, don’t let her walk, she can surely attack you or your impertinent dog that is not able to detect these warning signals that you’ve already detected.
Can all your pets and your iguanas live together? Absolutely.
Just as an iguana can live with a human being, taking all the right precautions and care, it can live with any animal. For example, iguanas are not carnivorous animals and they will not attack your exotic birds for a food interest, if they do it will be because you allowed them the space to approach when they were in an aggressive state and there if they open laments that could be avoided.
It is not only if your pet can live with other species, but if those other species can live with your iguana
Your home is your castle and your pets must follow your rules. They must learn and obey your feeding rules, sleeping hours, noise control, space control, etc.
A terrible idea would be, for example, to allow your dog or your cat to play in the terrarium of your iguana, that is their space and it is a call to disorder, chaos, and disorder, keep this in mind.