In this paper, we propose a learning algorithm that enables a model to quickly exploit commonalities among related tasks from an unseen task distribution, before quickly adapting to specific tasks from that same distribution. We investigate how learning with different task distributions can first improve adaptability by meta-finetuning on related tasks before improving goal task generalization with finetuning. Synthetic regression experiments validate the intuition that learning to meta-learn improves adaptability and consecutively generalization. Experiments on more complex image classification, continual regression, and reinforcement learning tasks demonstrate that learning to meta-learn generally improves task-specific adaptation. The methodology, setup, and hypotheses in this proposal were positively evaluated by peer review before conclusive experiments were carried out.