How do I get access to all summonable monsters at the lowest level?

Question

I want to build a character with every spell that summons creatures, without using Wish or magic items.

• This includes all conjuration spells that summon creatures, and all necromancy spells that make undead creatures.

• They don't need to summon everything simultaneously, so if a wizard
  had these spells in their spellbook, then it would qualify.

• Every summoned creature needs to have a stat block, so this does not include spells like Faithful Hound.

• No Unearthed Arcana.

What character (class levels, background, etc) do I need to do this? I want to achieve this with the fewest total levels, with multiclassing if necessary.

Option: Is it possible if you include magic items and Unearthed Arcana.

Answer 1

You can't quite catch them all

To simplify, I'll ignore the lower level spells which summon things which are also covered by higher level-more versatile spells. Eg. both conjure animals and woodland beings are supplanted by conjure fey because that can summon any of the creature the lower level spells can. If you want to include all of those spells, it makes it even less possible.

First, let's identify which spells we need:

• Conjure Fey, 6th level, covers beasts and fey

• Conjure Celestial, 7th level, covers celestials

• Conjure Elementals, 5th level, covers elementals

• Summon Greater Demons, 4th level, covers demons

• Infernal Calling, 5th level, covers devils

• Find Greater Steed, 4th level, has some monstrosity options which are unique

• Create Undead, 6th, Animate Dead, 3rd, for a slew of undead (Danse macabre is an alternative to animate dead)

• Create Homunculus, 6th level, makes an homunculus

• Pact of the Chain: Find familiar, allows the summoning of a pseudodragon which is not available by other means.

Doing this as a multiclass isn't possible because several of these only appear on one class list. Conjure celestial requires 13 cleric levels, find greater steed requires as many paladin levels, create homunculus needs 11 wizard levels. This is too many.

The workaround to this is Bard's Magical Secrets. However, none of these spells appear on the bard spell list and we don't get enough picks with it. A 18th level bard can take 6 spells (level requirements not a problem for this set of spells). Taking the College of Lore would get us 2 additional ones at 6th level, however these are only 3rd level spells (or lower) so only lets us pick up animate dead. It also doesn't get us Pact of the Chain: find familiar as that requires 3 levels of warlock.

Best we can do?

18th level Lore Bard from the Izzet league (GGtR; the availability of Ravnican backgrounds subject to DM/campaign)^†. Being from the Izzet league adds conjure elementals to our spell list. We pick up animate dead at 6th level and to stay on theme, probably conjure animals. With our normal Magical Secrets we take 6 remaining spells from the above list and take our losses on the pseudodragon as the last two Magical Secrets is worth more. This gets us all but one of the above spells and Pact of the Chain: Find familiar, which if we're dropping create homunculus means we're only losing out on 2 creatures (homunculus and pseudodragons).

This also doesn't get us all the supplanted spells (other than one 3rd or lower; above conjure animals): conjure animals, conjure woodland beings, summon lesser demons, find steed (covered by conjure fey, not its direct upgrade). You could grab find familiar using a feat, but not flock of familiars.

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† Medix2 points out that Mark of the Storm Half-Elf from Eberron: Rising from the Last War also adds conjure elementals to the class spell list. Same clause that the availability of Eberron content is dependent on DM/Campaign.

Answer 2

This is non-sustainable as more material comes out, but right now your best option might actually be a Lore Bard, who can snatch up to 8 spells from other spell lists over the course of his career.

I could only find 8 Conjure & Create spells that summon or create creatures in the compendium, so that should work out reasonably well.

It's extra amusing because the Bard gets none of these by default.

You'll need 18 levels to get all the spells, which is probably as good as it gets given how high level most of those summoning spells are anyway.

An example of how to collect your spells is this, although there's a bit of flexibility beyond 6th level:

6th (Lore Feature): Animate Dead + Conjure Animals

10th: Conjure Minor Elementals + Conjure Woodland Beings

14th: Conjure Elemental + Create Undead

18th: Conjure Fey + Conjure Celestial