Dynamic systems of interest can be complex and involve non-linearities, unobserved variables and multiple (potentially non-Gaussian) noises. These features complicate modeling and statistical analysis. We will consider statistical approaches to handle such analysis, paying special attention to stochastic volatility models with leverage. In this context, a likelihood-based analysis is difficult but can be facilitated by a recent contribution that exploits the idea of iterated filtering. We will present such an iterated filtering algorithm and illustrate its use for likelihood-based inference for general partially-observed Markov models. A key aspect of iterated filtering is that it is based on computer code to generate model realizations. This greatly facilitates exploration of model extensions by by-passing the need of additional analytical derivations. However, such “plug-and-play” exploration of model extensions can result in unexpected features, as we will illustrate with examples that arise when randomizing transition rates of continuous-time Markov chains.