In this paper we analyze the performance of random beamforming schemes in a multi-user Gaussian broadcast channel utilizing SINR feedback. For generality, the receivers are allowed to have multiple receive antennas. The first scheme analyzed allows each receiver to feed back the largest SINR it observes for each transmit beam. The distribution function of the maximum SINR is derived and is noted to differ from previous work. In an effort to further reduce feedback, a scheme where each user feeds back the maximum SINR observed over its receive antennas and transmit beams. Using the Fr´echet bounds and properties of chi-squared random variables, the throughput of this system is bounded and empirically shown to approach the performance of the previous scheme as the number of users increases.