  In this work, we find a Critical Energy induced Enhancement (CEE) mechanism
for the general three-body open-charm process at the $e^+e^-$ collisions, which
utilizes the peculiar kinematic behavior of the $e^+e^-$ annihilation process
involving three-body final states. We present a general analysis of a
three-body process $e^+e^-\to BC\to B(C\to DE)$. When the center-of-mass (CM)
energy of the $e^+e^-$ collision satisfies a critical relation
$\sqrt{s}=m_B+m_C$, there clearly exists the reflection peak of an intermediate
$C$ state near the threshold of the invariant mass distribution of $m_{BE}$ or
$m_{BD}$, whose formation is very sensitive to the CM energy. The reflection
enhancement phenomenon induced at the critical energy means that a new cluster
of charmoniumlike structures can be experimentally mapped. Taking an example of
$e^+e^-\to D_s^{*-}D_{s2}^*(2573)^+ \to D_s^{*-}(D^0K^+)$, we further
illustrate this novel phenomenon when $\sqrt{s}=4.680$ GeV. What is more
important is that a series of optimal CM energy points to search for new
charmoniumlike structures in three-body open-charm processes from $e^+e^-$
annihilation are suggested, which can be accessible at BESIII and further
BelleII as a new research topic.
