  A model for the reaction $\gamma p\to\rho^-\Delta^{++}$ is presented with the
$t$-channel $\pi+\rho$ exchanges reggeized to describe the reaction up to high
energies. Gauge invariance of $\rho$ exchange is discussed in connection with
the convergence of the reaction cross section at high energy. The roles of
electromagnetic (EM) multipole moments of $\Delta^{++}$ baryon and of $\rho^-$
meson are analyzed in total and differential cross sections and spin density
matrix elements. Photon polarization asymmetry $\Sigma$ is predicted for a
measurement of electromagnetic moments of $\rho^-$ and of $\Delta^{++}$.
