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Molecule optimization is a critical step in drug development to improve desired properties of drug candidates through chemical modification. We developed a novel deep generative model Modof over molecular graphs for molecule optimization. Modof modifies a given molecule through the prediction of a single site of disconnection at the molecule and the removal and/or addition of fragments at that site. A pipeline of multiple, identical Modof models is implemented into Modof-pipe to modify an input molecule at multiple disconnection sites. Here we show that Modof-pipe is able to retain major molecular scaffolds, allow controls over intermediate optimization steps and better constrain molecule similarities. Modof-pipe outperforms the state-of-the-art methods on benchmark datasets: without molecular similarity constraints, Modof-pipe achieves 81.2% improvement in octanol-water partition coefficient penalized by synthetic accessibility and ring size; and 51.2%, 25.6% and 9.2% improvement if the optimized molecules are at least 0.2, 0.4 and 0.6 similar to those before optimization, respectively. Modof-pipe is further enhanced into Modof-pipem to allow modifying one molecule to multiple optimized ones. Modof-pipem achieves additional performance improvement as at least 17.8% better than Modof-pipe.