Randomized response techniques for estimating proportions of more than one sensitive attribute are proposed. The categories (attributes) need not necessarily be disjoint. There might be some overlaps among the categories; an individual may belong to more than one category. For example, an individual may have both HIV infection (one category) and tuberculosis (another category). The works of Christofides (2005), Lee, Sedory, Singh, 2011, A magical talk: Estimating at least seven measures of qualitative variables from a single sample using randomized response technique. International Statistical Institute: Proc.58th World Statistical Congress, 2011, Dublin (session STS001), 1948–1957.; Lee et al., Statistical Probability Letters, 83:399–409, 2013, and Arnab, Communications in statistics-theory and methods 52:94–103, 2023 for estimating the proportions of multiple attributes have been discussed in detail. Methods of estimating the proportions of each of the categories are also proposed. Expressions of the estimators of variances and their unbiased estimators are presented in detail for the various sampling strategies and RR models.