There are other possible solutions - I like legendary actions and even multiple reactions myself - but this one is a straightforward solution that doesn't require much mechanical manipulation.
As Sly puts it:
Each side in D&D combat has an overall number of actions they can take. If we have five characters in combat, that group has five full actions it can take. If the other side has ten orcs, those orcs have ten actions to the characters' five. That puts the action economy clearly in favor of the orcs. Even if the orcs are weaker, they have more actions which means they can do more stuff. That's the action economy.
When we think about boss encounters, we often focus on a single monster—like a dragon. In 5e, powerful monsters identified as legendary monsters have legendary actions which improve their action economy, often giving them the equivalent of maybe two to three full actions per round. Yet we sometimes assume that legendary monsters can stand off against four characters or more. If so, even with legendary actions, these monsters are still going to lose the action economy.
It makes perfect sense.
It also makes perfect sense that some bosses would have minions and bodyguards. Adding more monsters is a good solution for most cases.
On the other hand, you might want to give your players a lonely monster from time to time. Having minions as an option is great; making them obligatory is constraining.
But there is one way to "add more monsters to the fight" without actually adding more monsters: monster parts.
|...Better than one - Source.|
The exact mechanics are up to you. You can use something similar to the hydra ("Whenever the hydra takes 25 or more damage in a single turn, one of its heads dies"), any "called shots" rule you like, a "bloodied" condition that depletes your foe when it reaches half HP, making the enemy suffer after being hit with a natural 20, or something unique to your game.
The important part is that the boss loses some of its attacks as the fight goes own - exactly as if it were a bunch of smaller enemies - and that the PCs know that they can make the monster weaker.
It is easy to explain the situation to your players if the monster has three heads, a dangerous tail, or multiple eye-stalks. For example, you can give your 3rd level party a Chimera to fight, split the HP, and let them tell you which head they are targeting with each attack.
|More fun than a bag of HP! - Image copyright WotC|
Here is a list of effects you might add for a multi-part creature:
* A big monster suffers more damage from an area effect than a small one. Or not.
* A monster part can be target with a reaction from the PC being attacked.
* A monster loses the ability to escape after having their wings or legs hurt.
* A monster loses the will to fight as the number of attacks is diminished.
* A hacked monster part becomes a weapon.
* Damage that exceeds the maximum damage a body part can take is wasted - which both allows the monster to live longer and make the PCs accomplish something. You can also allow the PCs to use their cleave-like abilities when they reduce a body part to 0 HP.
Some people prefer to make the stakes rise as the fight goes, but I'm not so sure this is the ideal solution; it seems to me that hurting the PCs a bit and then deal less damage as they are low on HP might be better than a few annoying hits and then bringing in the big guns as the PCs are hurt. Making the big monsters a bit less dangerous as the fight goes mirrors most of the PC's tactics well (when first encountering a boss monster they will usually spend all their powers).
With that said, I'm all for mixing things up from time to time. Let some monsters get more dangerous when they're hurt!
Another cool thing is that if the PCs are near death and see no changes in their opponents... they know it is time to run away! Ideally, the decreasing damage per round will avoid a surprise TPK... most of the times.
But you wanted a BOSS monster, didn't you?