Multi-task optimization (MTO) has emerged as a new growing field and has elicited numerous related studies. However, most existing MTO algorithms are overwhelmed by many-task optimization (MaTO) problems due to the complex inter-task relationships. To overcome this challenge, a novel evolutionary framework towards MaTO namely MaTEA-AAT is proposed in this paper. First, a new transfer paradigm called adaptive asynchronous transfer is used to improve the transfer efficiency. Second, a selection strategy is devised to choose the proper transfer task pair from the plethora of inter-task relationships. Finally, an experiment is designed to compare with four different types of algorithms on the CEC2021 many-task test suite and the results demonstrate the advantage and compatibility of MaTEA-AAT.