Current behavior
Users can Mute notifications (T150419) and direct emails (T138166) from individual users in their preferences. At the moment, this only applies to the wiki where the preference is set. (For example, if I block User:Foobar on English Wikipedia, he can still email me on Japanese Wikipedia if I have made edits there.)
Community Tech is currently building T16950: [Epic] Support global preferences on Wikimedia wikis which may be an avenue.
Proposed change
Build a global (cross-wiki) unified Mute feature that works for both Notifications and Special:EmailUser. This will likely need to be a Special: page.
We will also have to determine a migration strategy from the existing Mute lists to the new mute list.
Options were investigated by @dbarratt in T171624: Investigate making Mute cross-wiki