When we say “They get along like cats and dogs,” we mean they don’t get along at all.

But the idea that cats and dogs are natural and permanent enemies is not necessarily true.

There is always the potential for conflict between two (or three, if you add humans in the mix) species who have differing habits and communication styles. But pets that live together can indeed learn to live together in peace.

According to a survey by the American Pet Products Association, 46 percent of households with pets have multiple types of animals. Cats and dogs are the most common combination, found in 32 percent of pet-owning households.

In homes where the humans are away all day, a dog and cat can keep each other company and often play and sleep together, groom each other, and team up to get in trouble.

But how you introduce a new pet to your menagerie is key to establishing peaceful coexistence — or even friendship — among pets.

Start with scent: Introduce your pets by scent first, not sight. When you bring a new cat home, for example, isolate it in a small room for a few days with everything it needs: food, water, litter box, toys. Its scent will drift out to your dog, and the cat can get used to your dog’s scent, as well. After two or three days, let the cat explore the house while the dog is in the yard or on a walk with someone else.

Maintain control. It’s never a good idea to just turn animals loose and hope for the best. That’s a recipe for fear, anxiety and stress on the part of all involved. Have your dog on a leash, and make sure your cat has an escape route.

“Having ample getaway spaces for cats, such as tall cat trees or gates with a cutout that the cats fits through but not the dog, is essential,” says Mikkel Becker, an animal trainer and co-author of the upcoming book “From Fearful to Fear Free.”

A dragline attached to a harness can help to prevent bolt-and-chase sequences during the settling-in period, Becker said. Until you’re sure pets are getting along, supervise interactions and separate them when you’re not around.

Use a reward system. Give treats liberally to both parties. Reward your dog when it stops barking or growling at the new cat. You want both pets to think that being in the presence of the other is a good thing.

Dog trainer Liz Palika has fostered many litters of kittens with the aid of her English shepherds. Her best piece of advice in one word? Patience.

“A friendship between a dog and a cat cannot be forced,” she says. “Let them gradually get to know each other and provide safe places where they can get away from each other.”