How about extending the season to 35 days - An extra week for an extra competition.

Either then have the first week or last week of the season for 2 extra cup competitions - or space them through the season.

Have the Cup how it normally is.
Have the CL how it normally is.
Have the League how it normally is.
Have a Cup where everyone is on the same level (So if you are level 20 everyone else in that cup is too - instead of how it currently is where its based on squad strength)
A Cup winners cup/League to fit in too.