In sample surveys with sensitive questions, randomized response techniques, like the unrelated question methodology, have a huge advantage in estimating population proportions by adjusting for non-response or untruthful response. In reality, multiple sensitive proportions from small areas could be of great interest. Therefore, we consider using the unrelated question design with multiple sensitive questions and single random mechanism. Given combined binary response data, we can construct a hierarchical Bayesian model with latent variables to get more accurate estimates. There is also a computing challenge since we need to estimate parameters from all stages of the model. Thus, Markov chain Monte Carlo methods are applied to predict the finite population proportions of sensitive attributes. We compare the estimation error under different area size and correlation between the two sensitive questions during the simulation study. In the end, an application on body mass index data from the Third National Health and Nutrition Examination Survey is provided to verify our procedures.