We introduce the MORE-Q dataset, a quantum-mechanical (QM) dataset encompassing the structural and electronic data of non-covalent molecular sensors formed by combining 18 mucin-derived olfactorial receptors with 102 body odor volatilome (BOV) molecules. To have a better understanding of their intra- and inter-molecular interactions, we have performed accurate QM calculations in different stages of the sensor design and, accordingly, MORE-Q splits into three subsets: i) MORE-Q-G1: QM data of 18 receptors and 102 BOV molecules, ii) MORE-Q-G2: QM data of 23,838 BOV-receptor configurations, and iii) MORE-Q-G3: QM data of 1,836 BOV-receptor-graphene systems. Each subset involves geometries optimized using GFN2-xTB with D4 dispersion correction and up to 39 physicochemical properties, including global and local properties as well as binding features, all computed at the tightly converged PBE+D3 level of theory. By addressing BOV-receptor-graphene systems from a QM perspective, MORE-Q can serve as a benchmark dataset for state-of-the-art machine learning methods developed to predict binding features. This, in turn, can provide valuable insights for developing the next-generation mucin-derived olfactory receptor sensing devices.