  Motivated by concerns regarding possible two-body contributions to the
recently-measured inclusive $\Upsilon$(nS)$\to\gamma+X$ direct photon spectrum,
we report on a preliminary new study of exclusive radiative decays of the
$\Upsilon$ resonances into two-body final states ${\cal R}\gamma$, with ${\cal
R}$ some resonant hadronic state decaying into four or more charged particles.
Such two-body processes are not explicitly addressed in the extant theoretical
frameworks used to calculate the inclusive direct photon spectrum. Using data
collected from the CLEO III detector at the Cornell Electron Storage Ring, we
present upper limits for such $\Upsilon({\rm 1S})$, $\Upsilon({\rm 2S})$, and
$\Upsilon({\rm 3S})$ two-body decays as a function of the recoil mass $M_{\cal
R}$. Additionally, we place upper limits on the cross-section for ${\cal R}$
production via radiative return for center-of-mass energies just below the
$\Upsilon({\rm 1S})$, $\Upsilon({\rm 2S})$, and $\Upsilon({\rm 3S})$ energies.
The results presented in this document are preliminary.
