  We provide the first example of continuous families of Poincar\'e-Einstein
metrics developing cusps on the trivial topology $\mathbb{R}^4$. We also
exhibit families of metrics with unexpected degenerations in their conformal
infinity only. These are obtained from the Riemannian version of an ansatz of
Debever and Pleba\'nski-Demia\'nski. We additionally indicate how to construct
similar examples on more complicated topologies.
