  We prove $L^p$ estimates for trilinear multiplier operators with singular
symbols. These operators arise in the study of iterated trilinear Fourier
integrals, which are trilinear variants of the bilinear Hilbert transform.
Specifically, we consider trilinear operators determined by multipliers that
are products of two functions ${{m}}_1(\xi_1, \xi_2)$ and ${m}_2(\xi_2,
\xi_3)$, such that the singular set of $m_1$ lies in the hyperplane $
\xi_1=\xi_2$ and that of $m_2$ lies in the hyperplane $\xi_2=\xi_3$. While
previous work \cite{MTT2} requires that the multipliers satisfy $\chi_{\xi_1
<\xi_2} \cdot \chi_{\xi_2<\xi_3}$, our results allow for the case of the
arbitrary multipliers, which have common singularities.
