I was once locked out of some pretty important accounts while traveling overseas. Ever since then, I've been thinking about the importance of being able to "shard" both secrets and authority.
If I were to be imprisoned, for example, I might want my lawyer and family to be able to access all of my emails from two years ago up to one week ago. If I were to suddenly die, I would want my family to have full access to all of my accounts, with little hassle.
I would like to be able to tell my email provider (through my account settings) that if at least two people out of each of these three groups agree that such-and-such condition has been met, then these people will be granted this sort of access. The process would notify the other members of the groups I defined and have a delay to allow some kind of veto/vote if there is any disagreement. It may be a bit fiddly, but if a standard were defined for how the interaction works from a user's perspective (including steps to make sure you understand the consequences of how you've configured it), at least it could work consistently across all kinds of accounts.