A lot of people ask, if I get another pet will she get along with my pet? There is no simple answer to this question, but there are some facts to consider that might help forecast the results of such interspecies interactions: The species of the housemate you intend for your cat (or proposed cat)
The temperament of the individuals to be mixed
The early and later experience of the individuals to be mixed
Which species is the resident animal
Our own ability to monitor and manage the situation
The environmental setup
While there can be some very harmonious marriages of species, in other cases the result of the mix can be damaging to one or both animals, or even lethal.
Cats and Dogs
Former President Clinton found out that bringing a dog (Buddy) into the White House where there was already a cat (Socks) was not as easy as balancing the U.S. budget. The two fought like, well, dog and cat. But do all dogs and cats hate each other? The answer is no. The relationship between these traditionally acrimonious species can range from good friends, to indifferent, to positively hostile.
There are genetic influences on the relationship. Dogs, by nature, are predators. Predators tend to chase rapidly moving and furry things smaller than they are ... and that is the job description of a cat.
So there is a potential problem. But dogs and cats, like humans, are not driven by nature alone. There is also a learned component to what they do. For a dog and cat, there is a sensitive time period when they learn who their friends are. This time period spans the first 2 to 3 months of life.
A puppy that is raised with cats during this time, and experiences no adverse consequences of the interaction, will likely grow up to regard cats as benevolent domestic fixtures. The reverse is also true. It may be slightly easier to introduce a new kitten to a resident dog than to introduce new puppies to a resident cat because of the highly territorial and antisocial nature of some cats.
But you can also have your work cut out introducing kittens to a highly predatory species of dog. Both situations can be managed by proper chaperoning and protection of the most vulnerable species. Time spent together may even result in a level of mutual tolerance, if not mutual admiration. If puppies and kittens are raised together, neither party should present a problem when integrating with the opposite species, unless the incumbent is particularly mean.
Cats should not be introduced to a home with dogs that have chased and tried to kill cats. These dogs will probably find it difficult to see cats as anything other than prey, and even if they do not actually manage to catch the cat, may make her life pretty miserable. Likewise, a puppy may have to be protected from a territorial bully of a cat that has, by virtue of prior experiences, or lack thereof, a lifelong hatred of dogs or wishes to walk alone. Sometimes a dog in such a situation will learn to avoid a dangerous cat. In other instances, the cat may spend her life in trepidation of the dog. Neither of these situations is desirable or reasonable and they should, if possible, be avoided by prevention or rehoming of one or other of the feuding parties. That's what happened to Socks.
Cats and Pocket Pets
Mice, rats and other small critters should only be kept in a home with cats if you can guarantee to provide for their welfare. However interested and benevolent your cat may appear to be toward the rodent or rabbit, don't believe it. Cats just can't help themselves. Nature has programmed cats to chase after and pounce on small animals that run quickly. If you do want to have mice or rats in the same house as a cat you have to make sure that:
The bars of the cage are close enough together to prevent Houdini moves by the little ones.
The cage is not constructed of anything they may chew through.
The cage cannot be knocked down or over by the agile cat so that the door springs open, exposing the inmates.
It is said that rats over 500 grams weight can take care of themselves, but I wouldn't trust my life, or the rat's life, to that saying.
Cats, Birds and Fish
The same applies to birds and fish. The birdcage and fish tank should be firmly secured and be well out of harms way. Fish and cats are not too bad a combination, as long as you can literally keep a lid on things – but with cats and birds, the situation is more problematic. While fish usually remain untroubled by the periodic, riveted attention they receive from cats, birds are not so immune to their predatory onlookers' stares and can become quite troubled. Also, it's a little easier for a cat to tip over a birdcage than to heave over a fish tank. Larger birds, like macaws, may not be easy to intimidate and may even give the cat cause for concern, but small avians, like parakeets, are definitely at risk of chronic intimidation, and are even at risk of injury or death. And they usually know it. Not a very nice predicament for the caged ones and one to be avoided at all costs.
Cats and Snakes, Reptiles and Chelonians
There is no possibility of social harmony between cats and the above species. Snakes, etc. should be housed alone and cats should be protected from them. Larger constrictor snakes and poisonous snakes can easily kill cats. Reptiles, like iguanas, can be very aggressive and have sharp teeth. Beware the cat that takes on a large iguana. Tortoises can look after themselves in ways for which they are famous, but why allow them to be hassled by a curious cat who gets perverted pleasure in seeing the chelonian's head go shooting back under the shell. There have to be other ways a cat can entertain herself.
If you are thinking of mixing species, find out what each species does for a living in the wild. Ask if they are predatory, aggressive, territorial, solitary, gregarious, and so on. That will give you some idea what to expect. Then ask, how the species was raised, with whom, by whom, where and when. Next, you should probe for any information about prior interspecies interactions of the species in question (if that's not already moot).
Finally, if you are still up for it, insist on a trial marriage before you commit to the newcomer. Not every creature gets along well with others, but then again, not every creature enjoys the solitary life. Sometimes you just have to try putting pets together to find out. But be safe. Pets' lives are in your hands. With the correct early socialization, seemingly miraculous unions can be engineered. Cats that allow birds to perch on their heads, cats that allow mice to run all over their bodies, even when they're nursing (there's another generation of mouse friendly cats in the making), and cats who allow themselves to be groomed by non-human primates. It all smacks of "and the lion shall lie down with the lamb" (also possible), as well it might, but please, never trust your cat with a snake or a reptile.