@Yotus already brought up some fine points, but one that I was surprised not to see was:
This is an existing mechanic that can be easily adapted to your specific monster. Take a look at dragons, vampires, liches, and just about any CR >15 monster, and you'll find legendary actions. These are actions a monster can do out of turn. They're usually fairly basic. Some examples are:
move (usually with a free disengage on that movement)
make a single melee attack
do a single target/AoE debuff/damage effect (usually costs multiple legendary actions)
you can think of these as monster reactions, except they don't need triggers, and you are limited to 3 per turn rather than 1, and the monster still gets their reaction for an opportunity attack/counter spell/whatever.
These extra actions can help them gain ground on the squishier ranged characters/casters, lock down their heavy hitting opponents while attacking the support characters, or do some extra damage between turns. It almost makes it like there are 2 opponents there.
As a bonus, because they are at will, you can use them to control the fight a bit. If the fight is going to easy, you can 'forget' that your boss has legendary actions, and odds are your players won't remind you. If it starts swinging back their way too much, make a quick change, and your guy now gets 4 legendary actions on his turn, rather than just 3. Sure, its a bit railroad-y, but it will help you balance the fight on the fly.
Roll your boss into Initiative twice
This isn't technically an existing mechanic, but its really quite simple. It works best for your skirmisher types: the quick agile boss, rather than the big lumbering one.
Just roll initiative for your boss twice, and put him in the turn order twice. He gets 2 turns, and two reactions, but otherwise works just the same way. Mechanically he is 2 people who have the same AC, have the same movement speed, always stay in the same square together, and have a shared health pool (like a 2-way warding bond).
In order to properly balance this encounter, calculate the effective XP of the fight as if there were 2 NPCs with 1/2 the health of your boss. This is literally what it is, it's just that they share the same HP pool.