Like orchids and bromeliads, the Swiss cheese plant is an epiphyte that grows on another plant but isn’t a parasite. Because it can become so large, Swiss cheese plant typically is grown as a floor plant. Elvira Kashapova // Getty ImagesHow to Care for Swiss Cheese PlantThe Swiss cheese plant is an easy-care, vigorous plant if given the right conditions. Tatiana Lavrova // Getty ImagesProblems with Swiss Cheese PlantsSwiss cheese plants are super-hardy and rarely have issues. Unfortunately, all plants that go by the common name of Swiss cheese plants are toxic to pets, according to the ASPCA.