In inertial confinement fusion (ICF), overlapping of laser beams is common. Owing to the effective high laser intensity of the overlapped beams, the collective mode of stimulated Brillouin scattering (SBS) with a shared scattered light wave is potentially important. In this work, an exact analytic solution for the convective gain coefficient of the collective SBS modes with shared scattered wave is presented for two overlapped beams based on a linear kinetic model. The effects of the crossing angle, polarization states, and finite beam overlapping volume of the two laser beams on the shared light modes are analyzed for cases with zero and nonzero wavelength difference between the two beams. It is found that all these factors have a significant influence on the shared light modes of SBS. Furthermore, the out-of-plane modes, in which the wavevectors of daughter waves lie in different planes from the two overlapped beams, are found to be important for certain polarization states and especially for obtuse crossing angles. In particular, adjusting the polarization directions of the two beams to be orthogonal to each other or tuning the wavelength difference to a sufficiently large value (of the order of nanometers) are found to be effective methods to suppress the shared light modes of SBS. This work will be helpful for comprehending and suppressing collective SBS with shared scattered waves in ICF experiments.