The total 'season' days can be extended from 28 to 30. A rest day would be very helpful in between the end of one season and the start of the other season.
So, briefly, 28 days for playing the current competitions, 1 day for the Super Cup, and 1 day for the pre-season. The Super Cup can be played on day 30 of the same season, and the pre-season (no competitive matches set) can be on day 1. Competitive matches begin as from day 2.
P.S.
Or add a week that can be used for recovery, recruitment and a pre-season tour.