What DnD 5e build (with minimum number of combined levels over all classes) is needed to summon all summonable monsters?

What build would make if you just want to be able summon all monsters (of the summonable monsters) without a general purpose spell like wish or special equipment – how many levels of a multiclass do you need at minimum? Specify background. I believe a Wizard (Summoning school) can nearly summon all monster types with CR limits but for instance has to choose between demons and animals at level 4.