All D20, but DnD 5 especially, are designed and balanced assuming a 4 or 5 player party. And you can kinda tell, when the rules start asking you to apply multipliers to bigger parties, rather than giving any concrete guidelines. Assuming distributed player competence, a 6 person party isn't simply 20% stronger than a 5 player party. It's much higher. There's an entire additional PC, with their own suite of abilities, magic items, and most importantly, actions. Never underestimate the power of having more standard actions than the other guys (unless you're a pack of CR1/2 minions going up against a bunch of level 5 adventures, then you're screwed either way).
In short, designing challenging encounters for big parties is one of the more substantial challenges a GM may have to face. There seems to be a razor thin design space between "no actual danger" and "guaranteed TPK" when planning for large parties. My own personal strategy is "5 players per party max unless you have a super good reason that a sixth needs to be in this particular game, and never ever ever ever more than that (and preferably not 6 for long)," but that probably won't help you, specifically.
First of all, stop giving them one big thing to focus on. There are a couple iconic encounters that tend to necessitate one big monster against a party of intrepid heroes, like dragon slaying. The problem here with big parties is 1 creature generally can only attack one thing at a time, so even if the beastie is downing 1 PC a round, the rest of the party can pop cool downs and beat the timer. If you design the combat space so the beastie can use it's AOE abilites to good effect, you often find yourself looking at a TPK. Quantity may be a quality all it's own, but it isn't everything. Basically, when the party is that big, the single monster encounter HAS to be able to one round KO any given PC, or it's not a threat. And while it's killing one PC a round, the remaining party members HAVE to have a DPR high enough to whittle the beastie down before it kills them all, or they all just die. SO! Anytime you're tempted to let 7 or 8 dungeon crawlers dogpile one big boss monster, resist the urge. Instead of fighting one wyrm, why not a mated pair of adults, maybe with a wyrmling thrown in to harass the squishies? (Actually, this particular piece of design advice sort of holds true for any size party if there's more than one healer to keep the front liners standing)
Secondly (related to the first), if your party outnumbers the monsters, they'll probably win unless each monster is SIGNIFICANTLY stronger than the PC. I can't give concrete CR equivalencies because it's different at different power bands, but 7 lvl 5 PCs who know which end of a longsword is pointy should mop the floor with 5 CR7-8 monsters. The power of two players worth of extra actions is too substantial to ignore. Design the encounter using the guidelines in the DMG, then add a few support casters or bowmen(or bowwomen, or bowgoblins, or bowwhatevers) at a little under CR to bring the numbers within 1 of the party.
Finally, if you're going to do mob (mob in this context being a large angry group, not a MMO enemy, nor a crime family) encounters, consider looking at the minion style monsters from 4th edition. They had decent defenses and attack bonuses, but 1 HP and very low damage. Custom brew up something mob-able, maybe give them advantage for being adjacent to allies, with a decent attack bonus and a beefy AC, but a damage range of a d3 and very low health. And remember, mob fights aren't typically meant to be challenging in and of themselves, they should be hard enough to drain some resources while letting the players feel like badasses for steamrolling through a pile of enemies. Remember, damage spread to 7 players hurts a party much worse than that damage stacked on 1 or 2 frontliners.
Demons summon demons
See the "Variant: Demon Summoning" sidebar on MM. p. 54:
Some demons can have an action option that allows them to summon other demons.
Summon Demon (1/day): the demon chooses what to summon and attempts a
magical summoning. {A few examples cited here for brevity}
- A glabrezu has a 30 percent chance of summoning 1d3 vrocks, 1d2 hezrous, or one glabrezu.
- A marilith has a 50 percent chance of summoning 1d6 vrocks, 1d4 hezrous, 1d3 glabrezus, 1d2 nalfeshnees, or one marilith.
- A nalfeshnee has a 50 percent chance of summoning 1d4 vrocks, 1d3 hezrous, 1d2 glabrezus, or one nalfeshnee.
- A vrock has a 30 percent chance of summoning 2d4 dretches or one vrock.
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:
30% chance of summoning 1d3 vrocks, 1d2 hezrous, or one glabrezu.
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.
A summoned demon appears in an unoccupied space within 60 feet of its
summoner, acts as an ally of its summoner, and can't summon other
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.
Best Answer
Using an online Challenge calculator, I am not seeing the issue that you are describing.
Monsters exist up to CR 24, and then the Tarrasque by itself is 30.
For 4 Level 20 PCs, a single enemy of CR 23 is at the high end of a Hard encounter, just barely below the threshold for a Deadly encounter. A CR 24 is thus a Deadly encounter, but 5 Level 20 PCs push it back down to a Hard. (The Tarrasque requires 7 Level 20 PCs to push it under the Deadly level, but lets ignore that one! Using that, you are definitely threatening a TPK!)
I believe you are calculating challenge improperly. I will explain what I think you are seeing, and you can obviously correct me if I am off base.
For the CR calculations(using the table on page 82 of the DMG or page 56 of the Basic DM Rules), a level 20 PC has a Deadly threshold of 12700 XP. A single CR 15 monster is worth 13000 XP. Since that is higher, you see it as being a Deadly encounter. However, for encounter calculations, you must add in the XP threshold for each party member to arrive at your overall thresholds (which is explained in step 2 of the Evaluating Encounter Difficulty section on the same page as the XP Chart). For a party of 4 Level 20 PCs, the Deadly level is set at 50800 XP. A single CR 15 monster against a party of 4 Level 20 PCs will be an Easy encounter.