LoRa has seen widespread adoption as a long range IoT technology. As the number of LoRa deployments grow, packet collisions undermine its overall network throughput. In this paper, we propose a novel interference cancellation technique -- Concurrent Interference Cancellation (CIC), that enables concurrent decoding of multiple collided LoRa packets. CIC fundamentally differs from existing approaches as it demodulates symbols by canceling out all other interfering symbols. It achieves this cancellation by carefully selecting a set of sub-symbols -- pieces of the original symbol such that no interfering symbol is common across all sub-symbols in this set. Thus, after demodulating each sub-symbol, an intersection across their spectra cancels out all the interfering symbols. Through LoRa deployments using COTS devices, we demonstrate that CIC can increase the network capacity of standard LoRa by up to 10x and up to 4x over the state-of-the-art research. While beneficial across all scenarios, CIC has even more significant benefits under low SNR conditions that are common to LoRa deployments, in which prior approaches appear to perform quite poorly.