How to allow a existing key for a new purpose

In my did document, the initial key created was authorized for `authentication`.
I would like the key to also be valid for `assertion`, so I was curious how I would go about to update the document to add the key into the `assertionMethod` array?

If I look at this: https://github.com/decentralized-identity/ion-tools#generateoperationtype-contents-commit-async, I could use an `update` event, but after that I am confused if I should use the `addPublicKeys` object, where I would just use the same id (hence overwriting?) and specifying the purposes ( `['authentication', 'assertion']`?),

or should I use `updatePublicKey` via this interface: https://github.com/decentralized-identity/ion-tools/blob/9c6572daf91cc59f4bd489eb51da261d2483c0be/ion.js/lib.js#L172. Is the shape of the key object the same in both cases? How do I configure to pass through this object path: `op.previous.update.publicJwk`?

Thanks