A fascinating phenomenon in some sequential hypothesis testing problems: Working with less information can make testing easier. That is, constructing test martingales or e-processes in the canonical data filtration can lead to powerless tests, but working with the coarsened filtration (by eg transforming the data or looking at a subset of the data) can lead to powerful tests. This is the case in testing exchangeability, for instance.
Choe and Ramdas study how to combine e-processes that are developed in different filtrations.