Multi-objective optimization problems are ubiquitous in real-world science, engineering and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of non-dominated trade-off solutions, where the expensive objective functions are approximated as a surrogate model. In this paper, we propose a framework for implementing batched data-driven evolutionary multi-objective optimization. It is so general that any off-the-shelf evolutionary multi-objective optimization algorithms can be applied in a plug-in manner. In particular, it has two unique components: 1) based on the Karush-Kuhn-Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set; and 2) a batch recommendation approach that reduces the computational time of the optimization process by evaluating multiple samples at a time in parallel. Experiments on 136 benchmark test problem instances with irregular Pareto-optimal front shapes against six state-of-the-art surrogate-assisted EMO algorithms fully demonstrate the effectiveness and superiority of our proposed framework. In particular, our proposed framework is featured with a faster convergence and a stronger resilience to various PF shapes.