Marine plankton ecosystems are an important component of biogeochemical cycling in the oceans. Operational plankton functional type (PFT) models, that group plankton according to their biogeochemical properties, are currently being developed to resolve biogenic gas exchange between the ocean and atmosphere, and to model the lowest trophic levels in fisheries models. A fundamental problem with these models is that PFTs often go extinct in computer simulations, effectively removing the biogeochemical processes from the models. Cropp and Norbury [Cropp, R., Norbury, J., 2009a. Parameterizing plankton functional type models: insights from a dynamical systems perspective. J. Plankton Res. 31, 939-963] demonstrated that parameter combinations that allowed all PFTs to stay extant for all time in stable, homogeneous environments were rare in a PFT model with two competing phytoplankton and one zooplankton (NP1P2Z). In this paper, we examine the dynamical properties of a generic predator-predator-prey PFT model, and apply the analysis techniques developed by Cropp and Norbury to a simple example PFT model with one phytoplankton and two zooplankton (NPZ1Z2) in order to explore its properties and parameter space. We find that the properties of predator-predator-prey PFT systems are fundamentally different from those of predator-prey-prey PFT systems. The likelihood of parameter combinations for which all PFTs stay extant for all time in predator-predator-prey PFT systems depends critically on the process formulations used, and the properties of co-existing zooplankton (as defined by their parameter values) are quite different to those of co-existing phytoplankton.