I'm currently designing a 5th edition campaign with an antagonist who's sorta like this sociopathic mix between Jafar and the Joker. He's always got some plan to escape unscathed and has tons of strings he can pull to get his way. That's because he's this summoner who can creates hoards of elemental-based monsters to do his bidding, and he's a master at what he does. Despite this though, he isn't much of a heavy hitter himself, instead he just sics his own minions on his enemies.
I want the fight with him to be one where the challenge comes from fighting the sheer numbers and power of the monsters he summons, rather than from his great strength as a spellcaster. Are there any monsters like this in D&D I can use as a reference?
I'm aiming for a party level to be 15, maybe a bit above if necessary, by the time the final encounter happens.
As for the encounter itself, I'm hoping to make it just challenging enough to create a struggle, but not so challenging it might be considered "deadly".
Best Answer
Demons summon demons
See the "Variant: Demon Summoning" sidebar on MM. p. 54:
For your party's level, a CR 16 marilith ought to make for an interesting fight.
Caveat
If the marilith summons a lot of allies early in the fight, the fight turns from "CR appropriate" into "deadly and beyond" rather quickly as you add up the XP budget. That's very swingy. You seem to want a tunable encounter.
A more tunable encounter: glabrezu
Encounter budget hard for 4 x 15th level ~ 4300 x 4 = 17,200 XP worth of monster/NPC.
While it starts as a CR 9 fight, which is well below your party's threshold (5,000XP) look at who the glabrezu can bring to the party:
Let's say your glabrezu summons another one, that's two 5,000 XP monsters, times 1.5 = 15,000. Heading toward the budget for hard at this point.
Does the second demon summon more help? Let the pace and tempo of the fight tell you when to pull that trigger. If the party is all over demon number 1, call for more help. If they start cold, wait before the second demon calls for help.
Instead, summoning a few vrocks early to tune the fight to a difficulty to your liking may be a better pace for this party. Each vrock summoned is 2300 XP/CR 6.
How does that add up? (A review of DMG pages 80-84 regarding how to deal with the XP budgeting for your party would help as you work through this.)
The glabrezu summons 2 or 3 vrocks at the beginning, and you end up with your XP budget being 5,000 + 5,800 or + 8,900 multiplied by 1.5 or 2 as you see fit. As with the other answer, CR/XP math is inexact, particularly at high levels. 10,800 X 1.5 = 16,200 ; 10,800 X 2 = 21,600. The hard encounter is somewhere between those two numbers.
You are in the ball park for a hard to deadly encounter, and you don't have to roll the dice to see what the demon summons. You are the DM. Pick some demons to summon deliberately so that you can tune the encounter to your party.
Is this the only fight of the day?
Look at how many "adjusted" XP your party can handle, based on page 84 of the DMG. Adjusted XP per day per Character: 18,000. For a 4-person party, that's 72,000 XP worth of adjusted encounter monsters so let's go back to the marilith example.
The marilith summons another marilith.
16,000 + 16,000 X 1.5 ( two monsters) = 48,000. Within bounds, certainly.
Second marilith summons a glabrezu: (32,000 + 5,000) X 2 = 74,000. Almost dead on.
First marilith summons a glabrezu, who summons three vrocks: (16,000 + 5,000 + 8,900) X 2 = 59,800. Manageable.
First marilith Summons a nalfeshnee who summons 3 vrocks: (16,000 + 10,000 + 8,900) X 2 = 69800. With 4 vrocks it's 74,400.
What you have here is a tunable encounter basis. Rather than roll for a summons, I'd recommend that you tune the encounter with additional summoned demons to fit your party's experience level as players. You don't serve the rules, you are The Master of Rules (DMG p. 5). The rules serve you and your table in pursuit of fun.
Note: The variant Demon Summoning feature states that a summoned demon can not summon more demons.
Given that it's a variant rule to start with, and its purpose seems to be to avoid a never ending stream of summoned demons showing up if the dice get hot, we are still back to the DM using this feature to tune the encounter. Letting the dice drive the encounter from a hard-into-a-beyond-deadly encounter with a couple of hot rolls is letting the rules drive the DM, which is not the point of this edition of the game. If you want to only let the dice rolls drive the arrival of other demons, the difficulty of the encounter can go out of your hands. You have to decide, as a DM, if you are good with that or not.