  We report a fluctuation-driven state of matter that develops near an
accidental degeneracy point of two symmetry-distinct primary phases. Due to
symmetry mixing, this bound-state order exhibits unique signatures,
incompatible with either parent phase. Within a field-theoretical formalism, we
derive the generic phase diagram for system with bound-state order, study its
response to strain, and evaluate analytic expressions for a specific model. Our
results support the $(d + ig)$-superconducting state as a candidate for
$\mathrm{Sr}_{2}\mathrm{Ru}\mathrm{O}_{4}$: Most noticeably, the derived
strain-dependence is in excellent agreement with recent experiments [Hicks
\textit{et al.} Science (2014) and Grinenko \textit{et al.} arXiv (2020)]. The
evolution above a non-vanishing strain from a joint onset of superconductivity
and time-reversal symmetry-breaking to two split phase transitions provides a
testable prediction for this scenario.
