There is growing evidence that many Be stars are parts of binary systems. As the B-type primaries are very fast rotators and their spectral lines may be distorted by the circumstellar material, it is not easy to measure their radial velocity directly from the spectral lines. It has been shown that some Be binaries exhibit peak intensity variations consisting of double-peaked H$\alpha$ lines that are phase-locked with orbital periods. We searched for such variations in the spectra of 12 Be stars, including several known and suspected binaries. Our results include confirmation of the orbital periods in $\nu$ Geminorum, $ϵ$ Capricorni, $\kappa$ Draconis, 60 Cygni, and V2119 Cygni, its refinement in o Puppis, as well as suggesting hints for binarity in o Aquarii, BK Camelopardalis, and 10 Cassiopeae. Monitoring of the H$\alpha$ line profile variations in $\beta$ Canis Minoris for over the last 10 years gives further support to the existence of a 182.5-day period found earlier in a smaller set of data. A similar but still preliminary period (179.6 days) was found in the H$\alpha$ line profile variations in $\psi$ Persei. It is shown for the first time that $\nu$ Geminorum exhibits phase-locked variations in the H$\alpha$ emission peak intensity ratio and, therefore, is a part of the inner binary in this triple system. Our results show that the mentioned phase-locked peak intensity variations are observed in more Be binary systems than previously known and can be used to search for binarity of Be stars when application of other methods is inconclusive.