We present a general overview and the first results of the SUMO project (a SUrvey of Multiple pOpulations in Globular Clusters). The objective of this survey is the study of multiple stellar populations in the largest sample of globular clusters homogeneously analysed to date. To this aim we obtained high signal-to-noise (S/N > 50) photometry for main sequence stars with mass down to ˜0.5 M&sun; in a large sample of clusters using both archival and proprietary U, B, V and I data from ground-based telescopes. In this paper, we focus on the occurrence of multiple stellar populations in 23 clusters. We define a new photometric index, cU, B, I = (U - B) - (B - I), which turns out to be very effective for identifying multiple sequences along the red giant branch (RGB). We found that in the V-cU, B, I diagram all clusters presented in this paper show broadened or multimodal RGBs, with the presence of two or more components. We found a direct connection with the chemical properties of different sequences, which display different abundances of light elements (O, Na, C, N and Al). The cU, B, I index is also a powerful tool for identifying distinct sequences of stars along the horizontal branch and, for the first time in the case of NGC 104 (47 Tuc), along the asymptotic giant branch. Our results demonstrate that (i) the presence of more than two stellar populations is a common feature amongst globular clusters, as already highlighted in previous work; (ii) multiple sequences with different chemical contents can be easily identified by using standard Johnson photometry obtained with ground-based facilities; (iii) in the study of globular cluster multiple stellar populations the cU, B, I index is an alternative to spectroscopy, and has the advantage of larger statistics.