There are a number of mitigating factors to consider if you are thinking about adding another pet to your family, especially when attempting to intermingle cats and dogs. These animals are naturally prone to being wary of one another, and the ages and breed of the animals can also factor into whether or not they will be able to coexist.
The best time to bring a new pet home is when both creatures are young. However, your current pet may already be beyond this stage. Pet Place states that if one of the two is young, they can learn to accept the other's presence, especially if there are no major conflicts between them when the younger one is growing up.
However, this may still not be a guarantee of animal friendship. For example, Metro Animal explains that puppies are typically energetic and playful, but some cats may not want to participate in such things. This could create a rift between your pets, and if you are uncertain whether your current pet can adjust to sharing their home with another, you can always ask your vet for advice on how to proceed.
It's also important to discern whether you'll be able to afford the bills if you have to treat a sick cat and dog at the same time. Caring for multiple animals can be expensive, so it is best to make sure you are prepared for the added financial burden of a new pet.