The lack of parallax in the measurements is a big challenge in 3D image reconstruction for handheld Compton cameras. Our solution to this issue is to extend the conventional list-mode maximum-likelihood expectation-maximization (LM-MLEM) 3D reconstruction algorithm to allow the simultaneous use of multi-view Compton data seeking parallax improvement. It involves building a new list-mode simultaneous data space from multi-view Compton events, formulating the associated probabilistic models for the system response matrix and sensitivity, and developing an extended LM-MLEM algorithm. For the performance assessment, we experiment the extended 3D reconstruction algorithm on real multi-view data conducted with a handheld CeBr3 Compton camera developed by Damavan Imaging and a punctual 0.2 (MBq) 22 Na source. Various comparative studies with different view numbers, source locations and energy ranges confirm the outperformances of our extended LM-MLEM algorithm.