We introduce a first-ever algorithm for the reconstruction of multiple showers from the data collected with electromagnetic (EM) sampling calorimeters. Such detectors are widely used in High Energy Physics to measure the energy and kinematics of in-going particles. In this work, we consider the case when many electrons pass through an Emulsion Cloud Chamber (ECC) brick, initiating electron-induced electromagnetic showers, which can be the case with long exposure times or large input particle flux. For example, SHiP experiment is planning to use emulsion detectors for dark matter search and neutrino physics investigation. The expected full flux of SHiP experiment is about 1020 particles over five years. To reduce the cost of the experiment associated with the replacement of the ECC brick and off-line data taking (emulsion scanning), it is decided to increase exposure time. Thus, we expect to observe a lot of overlapping showers, which turn EM showers reconstruction into a challenging point cloud segmentation problem. Our reconstruction pipeline consists of a Graph Neural Network that predicts an adjacency matrix and a clustering algorithm. We propose a new layer type (EmulsionConv) that takes into account geometrical properties of shower development in ECC brick. For the clustering of overlapping showers, we use a modified hierarchical density-based clustering algorithm. Our method does not use any prior information about the incoming particles and identifies up to 87% of electromagnetic showers in emulsion detectors. The achieved energy resolution over 16,577 showers is σE/E = (0.095 ± 0.005) + (0.134 ± 0.011)/√(E). The main test bench for the algorithm for reconstructing electromagnetic showers is going to be SND@LHC.