Apply the longest duration timeout rather than overriding the previous.
It is a common occurrence for moderators to judge transgressions differently from each other, or from the broadcaster, and apply different timeout lengths. I feel moderators could benefit from having the timeout duration for the specified user not overridden by subsequent timeouts, but rather have a notice given to the mods specifying the remaining timeout for that person.
What would this proposal accomplish that overriding it with a longer duration doesn't already do?
Surely if there's inconsistency in moderation then the problem is the moderation team needing to communicate and coordinate better, and the streamer in question needing to lay out rules clearly.
It seems like this proposal would also make it more difficult to correct accidentally timing someone out for longer than intended.