In order to optimize the structure of the Message Passing Neural Network （MPNN）， reduce the number of iterations in the solving process， and improve performance of end-to-end neural Boolean SATisfiability problem （SAT） solvers， a More and Deeper Message Passing Network （MDMPN） was proposed. In this network， to pass more messages， an overall message passing module was introduced， thereby realizing transmission of additional overall messages from literal nodes to clause nodes during each message passing iteration. At the same time， to pass deeper messages， a message jumping module was incorporated to realize transmission of messages from the literal nodes to their second-order neighbors. To assess the performance and generalizability of MDMPN， it was applied to the state-of-the-art neural SAT solver QuerySAT and basic neural SAT solver NeuroSAT. Experimental results on the dataset of difficult random 3-SAT problems show that QuerySAT with MDMPN outperforms the standard QuerySAT with an accuracy improvement of 46.12 percentage points on difficult 3-SAT problem with 600 variables and iteration upper limit of 2¹²； NeuroSAT with MDMPN also outperforms the standard NeuroSAT with an accuracy improvement of 35.69 percentage points on difficult 3-SAT problem with 600 variables and iteration upper limit of 2¹².