Yes, it is possible, and it often happens in practice. For instance, the European Regulation 1143 on Invasive Alien Species (IAS) prohibits in Art 7 the acquisition and private possession of some invasive animal species (after a set date), and is a Negative List. These invasive alien species are therefore already prohibited to be kept or traded and can never appear on a Positive List of suitable pets. In general, the species on existing negative lists for private possession don’t need to be assessed for the Positive List, decreasing the workload for assessors. In that way existing Negative Lists can exist alongside a newly designed and implemented Positive List. The Positive List then helps to fill the gaps that are left by existing Negative Lists.