Open Problems talk:85
There came out a paper  that considers a very similar question. It does not solve this question explicitly but it would be worth looking at whether their methods imply a solution to this problem. At the very least, it is very relevant.
 Sample Amplification:Increasing Dataset Size even when Learning is Impossible; Brian Axelrod, Shivam Garg, Vatsal Sharan, Gregory Valiant; http://proceedings.mlr.press/v119/axelrod20a/axelrod20a.pdf