Differential meet-in-the-middle (MITM) cryptanalysis, introduced by Boura et al. at CRYPTO 2023, has been demonstrated to be an effective technique for analyzing the security of block ciphers. In this paper, we introduce an improved parallel partitioning technique, and incorporate it into a new framework with a flexible key recovery strategy. This framework is applicable to both SPN and Feistel ciphers. We apply the new framework to SIMON and Piccolo-128 for demonstration. In particular, we also develop an MILP-based tool for searching full attacks on Piccolo-128. For SIMON48/96, we propose the best attack, reaching 26 rounds against 25 rounds previously. For other versions of SIMON, we extend the best previous differential attacks by one or two rounds. In the case of Piccolo-128, while no current differential attacks show promising results, our differential MITM attack reaches 15 rounds, matching the same number of rounds of the best impossible differential attack.