We should have a 5-days week: A, B, C, D, E.
Weekend would be E and A.
12 months of 6 weeks each, except "February" with an extra week.
A would always the 1st, 6th, 11th, 16th, 21st, 26th or 31st (in "February").
B would always be the 2nd, 7th, etc.
Leap years would have a day F inserted between E and A at the end of "February" (of which it would be the 36th), keeping this new calendar consistent with the current one.
Very curious to understand the thinking behind this, why should the weekend be E and A? My first approach would be to have the weekend on D and E which would seem to be the end of the week.
You’d have to convince a lot of religious people to give up the day of rest they’ve considered a religious obligation for thousands of years.