The Queens Birthday (a public holiday) is on a different date in different commonwealth countries... so maybe not that wild a suggestion.
So this year, for instance, the calendar would go July 4 (Independence Day, Thursday) - July 1 (Friday) - July 2 (Saturday) - July 3 (Sunday) - July 5 (Monday).
[1]: https://kitchener.ctvnews.ca/canada-day-2015-13-places-to-ce...