  Given a complete theory $T$ and a subset $Y \subseteq X^k$, we precisely
determine the {\em worst case complexity}, with respect to further monadic
expansions, of an expansion $(M,Y)$ by $Y$ of a model $M$ of $T$ with universe
$X$. In particular, although by definition monadically stable/NIP theories are
robust under arbitrary monadic expansions, we show that monadically NFCP
(equivalently, mutually algebraic) theories are the largest class that is
robust under anything beyond monadic expansions. We also exhibit a paradigmatic
structure for the failure of each of monadic NFCP/stable/NIP and prove each of
these paradigms definably embeds into a monadic expansion of a sufficiently
saturated model of any theory without the corresponding property.
