A modular furniture system for use with cats includes shaped components and component connectors, to allow assembly in a configuration. The shaped components can be polygon shaped with right angles between segments, and flat rectangular side surfaces. The shaped components can be i-shaped, z-shaped, t-shaped, square-shaped, and l-shaped, can be manufactured from corrugated cardboard sheets that are glued together, and can further include a cover. Sides of the shaped components can be impregnated with a catnip solution to attract cats, which can use the modular furniture system for play and to scratch their claws.