My question is here: What DnD 5e build (with minimum number of combined levels over all classes) is needed to summon all summonable monsters?
I do not believe my question needs any changes.
The question is totally answerable if you consider the question as given and not try to make say something it doesn't like what class do want, do you want use all summoning spells, summon all monster.
Here is a possible solution using DnD Core only.
Given Summoning is kind of vaguely defined in D&D 5e- I just considered it as creating any monster in the monster manual
Druid 20 Cleric 9
Giving you Conjure Animals which allows 1/4,1/2,1,2 Challenge Rating beasts.
Conjure Celestial using 9th level spell slot which allows 5th CR Celestial
Create Undead which using a 9th level allows ghouls, ghasts, wrights, mummies.
Animate Dead which gives skeletons and zombies.
Can my question be reopened?