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• A new framework of multiple public goods games considering the persistence and transition of games is proposed. • The heterogeneous public resource of public goods game evolves with the persistence and transition of games. • Our new model can promote cooperation effectively, especially under the condition with scarce resource. Many various projects may exist in an enterprise in parallel, which leads to distinct group interactions. Team members cooperate in their respective projects, and sometimes it is possible to engage in several concurrent projects. Owing to practice makes perfect, the longer the duration of members participating in an identical project is, the higher benefits will be under same contribution. However, in a fiercely competitive environment, a huge conflict of interest between groups and individuals which results in social dilemma makes projects difficult to proceed smoothly. The experience of direct reciprocity shows that repeated interactions can alleviate this problem, but most multi-person dilemma studies consider a single game scenario, and public resources remain constant. Here we introduce a general framework of multiple public goods games. Taking the public goods game with threshold into consideration, public resource evolves with the persistence and transition of games. Our results suggest although collaborators are at a disadvantage in different game scenarios, our model can still effectively promote the overall cooperation in multiple public goods games. Especially, it performs better when public resource is relative scarce. [ABSTRACT FROM AUTHOR]