I like the idea of multiclassing being feat-locked.
Can you elaborate more on your idea of minimum level please?
4th level feat: Class initiate
+1 ASI
you gain all 1st level benefits of a multiclass of the class of choice as in PHB. You do not gain any HP or HD.
8th level feat: Class adept, requires class initiate
+1 ASI
you gain 2nd and 3rd level class features of the chosen class. Do not gain any HP or HD from those levels.
12th level feat: Class expert, requires class initiate and adept
+1 ASI
you gain 4th and 5th level feature of the chosen class. Do not gain any HP or HD from those level. Do not gain 4th level ASI from that class
16th level feat: Class master, requires class initiate, adept and expert
+1 ASI
you gain 6th, 7th and 8th level class features of the chosen class. Do not gain any HP or HD from those level. Do not gain 8th level ASI from that class
19th level feat: Class paragon
+1 ASI
you gain 9th, 10th and 11th level class features of the chosen class. Do not gain any HP or HD from those level.
If epic destiny or what ever makes a return at 20th level
then you can gain all class features of 12th, 13th and 14th class levels, even the ASIs instead of that boon if you have all 5 feats before.