How do you clear multiple Notification messages simultaneously

In the notifications dropdown, mouse over a grey header and select "Mark all as read". Is this what you were looking for?

That actually doesn't mark ALL as read, only 10 at a time.  I have 3000 notifications (as an admistrator/moderator) so I need a larger bulk option.

Looks like "mark all as read" actually marks only the visible items. So you can increase the number of visible items to mark more as read at a time. Go to Administration > Interface > Widgets > Site Banner  > notifications.vm and alter the pageSize near the top of the page. Note, this will alter it for everyone, so you might want to only temporarily increase this size. It may also be limited to 100 maximum pageSize.

Looks like "mark all as read" actually marks only the visible items. So you can increase the number of visible items to mark more as read at a time. Go to Administration > Interface > Widgets > Site Banner  > notifications.vm and alter the pageSize near the top of the page. Note, this will alter it for everyone, so you might want to only temporarily increase this size. It may also be limited to 100 maximum pageSize.