I think is just to much even for T11, if they would do something must be something not to hard for them and for the players.
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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.
+competitions = 5% condition every hour.