  Motivated by the generation of action principles from off-shell dualisation,
we present a general class of free, topological theories in three dimensional
Minkowski spacetime that exhibit higher-spin gauge invariance. In the spin-two
case, we recover a dual reformulation of the triplet system already known,
while the higher-spin systems that we obtain seem to be new. They are
associated with wild quivers. We study in which situations these exotic (or
strange) higher-spin models can be extended to dS${}_3$ and AdS${}_3$
backgrounds, revealing that the flat limit of such models, when they exist,
admits a one-parameter freedom. Interactions are studied in the simplest
higher-spin case featuring spin-2 and spin-3 fields. We then give several
higher-spin generalisations of these strange systems.
