  We present microscopic models of spin ladders which exhibit continuous
critical surfaces whose properties and existence, unusually, cannot be inferred
from those of the flanking phases. These models exhibit either `multiversality'
-- the presence of different universality classes over finite regions of a
critical surface separating two distinct phases -- or its close cousin,
`unnecessary criticality'-- the presence of a stable critical surface within a
single, possibly trivial, phase. We elucidate these properties using Abelian
bosonization and density-matrix renormalization-group simulations, and attempt
to distill the key ingredients required to generalize these considerations.
