  We combine several folklore observations to provide a working framework for
iterating constructions which contradict the axiom of choice. We use this to
define a model in which any kind of structural failure must fail with a proper
class of counterexamples. For example, the rational numbers have a proper class
of non-isomorphic algebraic closures, every partial order embeds into the
cardinals of the model, every set is the image of a Dedekind-finite set, every
weak choice axiom of the form $\mathsf{AC}_X^Y$ fails with a proper class of
counterexamples, every field has a vector space with two linearly independent
vectors but without endomorphisms that are not scalar multiplication, etc.
