When you first bring a new pet home, keep them in a separate room from your other pets. Introduce them slowly. This will help them get used to each other's smells and sounds without being too overwhelming. Allow them to sniff under the door and play together in short supervised sessions before letting them have free rein of the house. And as much as possible, introduce them to each other at the earliest age possible. Adult pets already has a routine they are used to so introducing a new addition to the family can be quite tough when your pet is already an adult. 

There are certain kind of pets/breeds that would be perfect for each other and would get along more than other pet combinations. Having the right combination of pets can make all the difference in a multi-pet household. If you're looking to add another pet to your home, do some research first on which breeds will get along best with your current pet. Though this is not 100% accurate because even pets of the same kind and breed can have different personalities, so make sure to get to know the pet you plan to add to the family personally. 

Pets need their own space to feel comfortable and safe. If they're constantly being crowded or jostled, it can lead to conflict. Generally, this is important especially for cats as cats need their own space to just chill and take a break from all the activities inside the house. You can create a space for them high up that they could feel secure and not to mention that cats love  high places and climbing as well. Make sure there is enough room for all of your pets to move around freely. 

Pets thrive on routine and predictability. Having set mealtimes, playtime, and bedtimes will help them feel more secure and less likely to lash out at each other. All pets need to know what is expected of them in the household. Make sure everyone is on the same page with regards to rules such as not jumping on furniture or stealing food from the table. Having consistent rules will help reduce conflict between pets. Each pet should also have its own toys to play with so that they don't have to fight over who gets to play with what and get them used to which is theirs.

If you need to discipline one of your pets, be sure to do it in a way that all of them will understand. This will help them realize that certain behaviors are not acceptable and will help prevent future conflict. If one pet can't do this, the other shouldn't also or this would cause confusion among them. Some might imitate the other pet's negative behavior. Make sure to also reward all f their positive behavior so the other pets would be motivated to imitate them as well. 

As mentioned earlier, though there are some known kind of pets/breeds that compliment each other, it all comes down to their personalities. To keep the peace in a multi-pet household, get to know each of your pet's personalities. Not all pets are alike, and understanding how each one behaves can help you anticipate conflicts and head them off before they start. For example, if you have a dog who is prone to getting jealous when you give attention to other pets, you might make sure to give her some extra tender loving care when another pet is around.

Observing all of your pet's body language every time is key to stopping a fight before it starts. Being observant is key to knowing whether a fight is about to break out so make sure you keep a close eye on them and see what certain situations do the other pet gets annoyed. Do your research about the meaning of every body language your pet makes like wagging their tail, lowering their ears, etc. to make sure you predict what each of them feels as well. Be on the lookout for changes in your pets' body language that could indicate they're feeling uncomfortable or threatened.

Avoid free feeding them all at the same time as some might tend to eat a lot faster than the other pet which might lead to them getting overweight and the other pet hungry. Instead, set a feeding schedule and stick to it to also avoid conflict because of food. This way, each pet will know when it's their turn to eat and they won't have to compete with the others for food.

It's important to find a veterinarian and professional groomer that are comfortable working with multiple pets. This will help to ensure that all of your pets stay healthy and properly taken care of. You can also consult them for behavioral problems between your pets so they can help you resolve it as early as possible before it even turns into a routine which will be hard to break!

Finally, make sure you're giving each of your pet enough attention. If one pet feels neglected, it may become jealous of the others and start acting out. Spend quality time with each of your pets every day to prevent this from happening. So before deciding to adopt lots of pets, make sure that you have the time to give them all the attention they need!