Ask Game Masters

I'm going to assume this is DND 5e, but this advice is system agnostic

Add objectives to your scenes that aren't "kill everyone else".

Add traps and environmental hazards to your scenes. Add enemies they can't kill.

Add a third faction that has its own goals

They need to get books out of the library before it burns down, while the crazed wizard and his fire elementals are doing a ritual that's going to make things worse for everyone.

The mansion is haunted, and this ball room in particular. Anyone who steps on the dance floor and doesn't dance is accosted by angry ghosts.

The room is filling with water. There are a series of levers to control the water. There are priceless works of macguffin that will be damaged by the water.

Each egg host killed explodes into a mist of parasites, potentially infecting everyone nearby. Some enemies don't care about being infected.

Security just wants everyone out, both the PCs and the cultists they're fighting. Security has powerful control abilities- a fire hose to push people, a sonic weapon to prone people. (Don't stun your players or prevent them from actually playing on their turn, but move them around and add costs to some actions)

Several NPCs are channeling spells. They are individually weak, but spread out. Each spell that completes adds consequences and complications. Perhaps they affect the current scene (eg: blow a hole in the wall allowing demons from outside to flow in) or maybe it affects the plot (they conjure a plague upon the player's home city)

I agree that alternative objectives are huge. Have some of the enemies be charmed friendlies and there is a cost to killing them. A portal that discharges high level monsters until a device is deactivated. A Darkness emitter is spreading, covering more of the battlefield every round and the enemies have Blindsight. A mage casts Wall of Stone down the center of the battlefield, splitting the fight. Some monsters have built in mini-objectives, like Hydras or Zombies

One of my favorite campaigns that I've run several times, the antagonists are a conspiracy of powerful undead who plan to undeadify a bunch of high-level characters and influential nobles (including a blue dragon, at one point), adding them to the conspiracy and creating more dangerous antagonists for the PCS.

At each stage of the game, the undead have several plans hatching all at once and it's difficult for the PCs to figure out what they all are and stop them. And they have to prioritize. There's also an Imperial senate they have to keep track of (like how many votes they have on their side versus how many votes their opponents have, both those under the influence of the undead and those just on the wrong side of the political game).

Each time they save someone, they add a powerful ally to their side, each time they lose someone... They now have a new dangerous enemy to worry about. By itself, this raises the stakes.

Here's some cool battles from that game... Each one is really nasty, but less so if the characters go in having done research and had previous successes. What makes them cool is that I spent the time to create the opponents... Not just stats but agenda, purpose and personality AND the consequences of winning and losing beforehand. The following monsters from 3.5 (that's the era where I created this game, but there's so much good material from all of those source books that you can go harvest for cool monster ideas).

1) Bone Naga.

One of my favorites. An arrogant young senator / nobleman (and potential regent / imperial heir, which is important) has had a statue of himself placed in the parkland outside the Senate building, where everyone has to see it walking to and from the Senate building.

The statue is actually hollow, and coiled inside is a bone naga, using detect thoughts to spy on all the senators (and the PCs).

To soften the PCs up if they mess with the statue during the day, the nobleman's guards confront them and start a fight. If they mess with the statue at night, they get in a fight with the nobleman himself (who is a psycho cultist who's been sacrificing teenage peasants to the devil he worships and who has a necklace that can summon lesser devils). The corpses of the sacrifice victims also rise as zombies (ghouls / ghasts - depending on character level) and join the fight if the PCS are stomping.

2) Vampire Ninjas

If you take the time to make the vampire ninjas as actual characters and think through their powers, they're actually super nasty and can totally TPK if you're not careful. Mist form / bat form combined with Ninja stealth and sneak attack? The vampires are trying to off the leaders of the local thieves and assassins guilds and take their place. Those two guilds are in a manufactured gang war started by one of the vampires (a halfling vampire assassin... Think about it. It's super nasty). You use sneak attack to hurt the big fighter badly right at the start of combat. If the vampires are getting pummeled, they go in and out of mist form and then sneak attack from mist form.

3) Blue dragon fight.

In my world, dragons of all colors used to interfere in politics all the time, but then retreated from the world for some reason. It doesn't matter why, what matters is that a blue dragon has started attacking imperial shipping after literally centuries of dragons leaving the humanoid world alone.

If the characters go stop the dragon the fight is deliberately a little bit too hard for them... Like they should lose at least one or two people if they do this (Even if those people get resurrected later).

However, if they're observant they may notice that the dragon seems to be unwell and sickly. If they managed to get it to stop fighting and talk to them, they will learn that the main big bad has promised it eternal life as an undead (and the dragon is pissed because it's dying had a stupidly young age... f or a dragon... of some mysterious illness). Of course, the big bad made the dragon sick. If they can cure it, they've made a powerful new ally. If they don't deal with the dragon soon enough, the big bad will show up at the final showdown riding a dracolitch lol. If they kill the dragon, the big bad will show up at the final showdown riding a zombie dragon that can still use its breath weapon.

There are some other really good scenarios in this campaign. An Eye of Fear and Flame and an army of specters are besieging one of the imperial relatives in his country estate. An entropic reaper has been summoned from the outer planes and is stalking and murdering the High-Ranking clergy of the imperial church. If they didn't deal with the cultist guy, he summons ice devils to attack the Senate building. If they DID deal with him, his father raises an army and marches on the capitol.

Oh right, another aspect of this game is that there are various military actions going on and if the PCS don't intervene in them, they end in massacres. And of course the dead soldiers are raised to join the ranks of the undead army. Also, Charnel Hounds and Boneyards are awesome aggregate undead... The more land battles are allowed to happen without PC intervention, the more hit dice the charnel hound has when it shows up. XD

The best thing you can do is give your players something to worry about other than the enemies. The room is filling with gas and players have to disable vents. Or artifacts in the room grant the enemies bonus or legendary actions, so the players have to destroy them or move them out of range. Or it's in pocket dimension and they have to complete a fetch quest through the enemies before the air runs out.

• Deplete their resources by putting the fight at the end of a dungeon or other chain of different kinds of encounters

• Higher level monsters

• Smart enemies. Sit down and think about what they do as if you were playing them in someone else's game. Dumb dragons land and get murdered, smart dragons stay in the air, flame the party, and have been abusing contingency spells for the last millennium.

• Stakes other than player death. Sure we can kill these bandits, but can we do it before they get away with the orphanage fund? What if they take hostages? What are we going to do about all these fires they set on the way in?

• Make it feel more dangerous than it is by use of good description. A hippo is a relatively low level monster, but when that one player that knows how scary they are IRL realizes what you're describing, they will crap their pants.

Try Villain Actions, a la https://nerdarchy.com/a-mouthful-of-5e-dd-villain-actions-inspired-by-matt-colville/

Some ideas:

Get them into multiple encounters within the long rest to exhaust resources. (Encounters don't have to be combat).

Try to give them other objectives in the fight so they can't play optimally. Chase the one carrying all the loot, or save the hostage.

You can just forcibly split the party, have a door come down so they are fighting two fights in two parallel corridors.

Change the crit rules (dangerous at low levels) we run on the rule where the second dice is always full damage to makes crits more dangerous and increase risk.

Challenging fights with a group that large are just going to have to take longer I think though.

Good luck!

Legendary actions, doesn't have to be amazing or have a whole bunch but the simple way of fixing the players being able to move 6-7 times and you only once is just making the monsters attack or move around more. Want it to be harder? Give the monster more legendary actions on the fly. Went too far? Have the wall collapse killing a few. This is the glory of the screen, the players have no idea what the encounter was supposed to be unless you tell them