Sure, but what weekday would it have? Would we have a repeated Sunday there?

Well if you want to keep the whole number of weeks thing, you are then doing a leap week every 7 years except for multiples of 28, or something like that. Or if you want to keep each week same number of days maybe a leap month.

Of course none of this is unheard of. The jewish calendar adds a leap month every 19 years to keep in sync with both the moon and the sun. Or if you want to go in the other direction you could just have one day not part of any week (cotsworth calendar)