To create vertical space for cats, consider adding a cat tower or placing a cozy bed or blanket on an elevated surface like a chair or couch. Cats enjoy perching and observing their surroundings, so positioning a perch near a window provides entertainment and a relaxing spot. You can also install shelves or ledges specifically designed for cats, allowing them to climb and explore. These elevated spaces offer both mental stimulation and a sense of security, catering to their natural instincts to climb and rest in high places.