Multiobjective multitasking optimization (MTO), which is an emerging research topic in the field of evolutionary computation, was recently proposed. MTO aims to solve related multiobjective optimization problems at the same time via evolutionary algorithms. The key to MTO is the knowledge transfer based on sharing solutions across tasks. Notably, positive knowledge transfer has been shown to facilitate superior performance characteristics. However, how to find more valuable transferred solutions for the positive transfer has been scarcely explored. Keeping this in mind, we propose a new algorithm to solve MTO problems. In this article, if a transferred solution is nondominated in its target task, the transfer is positive transfer. Furthermore, neighbors of this positive-transfer solution will be selected as the transferred solutions in the next generation, since they are more likely to achieve the positive transfer. Numerical studies have been conducted on benchmark problems of MTO to verify the effectiveness of the proposed approach. Experimental results indicate that our proposed framework achieves competitive results compared with the state-of-the-art MTO frameworks.