One of the big positives of 5E, is the simplicity of running the monsters, and the introduction of legendary actions and lair actions. I think if we are going to improve combat, the solution is not so much adding complexity, but adding variety and options.
I think the core question that should be addressed here, is why is the combat dull?
I've seen a few people say that there is not a whole lot of movement. You get into a melee, and you beat on the monster till it is dead. There is very little that forces (or encourages) you to change position. Wolves are a very simple example. All they do is run up to you and bite. Adding extra abilities (or modifications of existing abilities), or adding variations of existing monsters, could solve this issue.
Others have said that there's not a whole lot of encouragement to try something different. Once you start fighting, you repeat the same action round after round. I think this also ties into the issue of boring monster abilities. If the monsters keep doing the same thing over and over, without forcing a different action, nothing needs to change about the player strategy till the monsters are dead. Any injuries are easily healed, so tank and spank is the go to strategy.
I like the modular approach to design. Something that players can choose to add to existing monsters and their abilities, to make the fights more interesting. And I lean strongly towards the following:
-Monster formations: Templates for varieties of monsters (even wolves), that each specialize in something different. Players would be able to instantly add these templates to any group of monsters, to spice things up.
-New monster abilities: Abilities that force movement, or other combat actions. Or abilities that disable certain actions on a player. At the risk of making the running of monsters slightly more complex.
-Modifications to existing monster abilities: Also at the risk of making the running of monsters slightly more complex.
So here are some things I've come up with. A list of abilities/qualities that can be added to select monsters in a group, to make several of them have a unique role. For example, you could have one wolf with the meatshield ability, while another has acrobatic leap and chain attack or disperse. This would allow you to make a wolf leap in the middle of the party, and scatter them all. You could also have an alpha wolf with the leadership ability.
Movement related abilities:
These are abilities that allow the creature to more easily reach behind the front line.
Acrobatic Leap: As part of its movement, the creature can vault from any nearby wall, object or ally to jump into the fray. If it lands on an occupied square, that creature is pushed 5 ft. out of the square. With this ability the creature can also run across a wall as part of its movement.
Evasive roll: As part of its movement, the creature can move through an area occupied by an opponent, without provoking an attack of opportunity.
Forced movement abilities:
These are abilities that force the players to move.
Leap attack: If the creature leaps as part of its attack (provided it isn't already in close combat with the target), it automatically pushes the target 5 ft. back.
Disperse: The creature takes an intimidating action that forces all hostile creatures within 15 ft to dash 5 ft. away from it, and interrupting any concentration spells. Affected creatures can make a wisdom saving throw, equal to the creature's highest ability, to resist the effect.
Persistent breath weapon: If the creature uses a breath weapon, it can continue to breath it for as long as it chooses to, as long as it doesn't move from its position. It is however allowed to turn around and readjust its aim.
Lingering breath weapon: The breath weapon of the creature leaves a lingering effect that deals half the normal damage of the breath weapon. Fire breath leaves all the floor tiles (and water) that it hit on fire. Acid leaves puddles of acid, etc. These effects remain for the duration of the fight, unless removed.
Debilitating abilities
These are abilities that hinder the players.
Disarming bite: If the creature hits with a grapple-bite attack and gets a hold, it can immediately attempt to disarm its opponent with a strength check, and take the weapon for itself with its mouth.
Dust kick: If the creature starts or ends its movement near an opponent, it can kick up dust to blind the opponent. They must make a constitution save or be blinded for 1 round.
Cursed bite: When this creature hits with a bite attack, the target must save versus a curse.
Infectious bite: When this creature hits with a bite attack, the target must save versus poison.
Bleeding attack: When this creature hits with an attack, the target must save versus bleeding.
Tactics related abilities
These are abilities that encourage the players to change tactics.
Chain attack: If the creature hits with any of its attacks, it is allowed to make a free attack against another opponent within reach, that has not been attacked by it yet during this round.
Interlocking shields: If a group of creatures with shields forms a shield wall (by standing adjacent to one another), all attacks made against them are made at a disadvantage. Further more, all of them have the benefit of sharing the highest AC of any single member of their group.
Strength in numbers: As long as a group of creatures outnumbers their opponents, they enjoy the benefit of advantage on attacks and saves.
Leadership: As long as this creature is alive, he commands a group of minions who all get advantage on attacks and saves for as long as their commander is alive and within sight.
Spellshield: A group of spellcasting creatures can spend their turn (and each turn there after) blocking any and all spells against their allies. This ability manifests as a visible magical barrier in front of the group. If the concentration of any of the spellcasters is disrupted, the barrier is dropped. The barrier blocks only spells, not normal weapons or magically enhanced/enchanted weapons.
Spotter: As long as this creature is alive and able to speak, it can warn any allies within earshot, and make them immune to flanking.
Opportunist: If an opponent moves out of combat with this creature, it always gets to attack as a reaction. This negates the affect of the disengage action.
Necromantic touch: This opponent can touch one deceased ally on its turn as a full round action, to revive them as an undead. The undead ally retains all its normal abilities, but it is fully healed and now of the undead subtype.
Final strike: If the opponent dies, it gets one final attack against all creatures within reach. If the creature has a breath weapon, it may explode as its final attack, dealing the damage of its breath weapon to all creatures within range.
Clever girl: If the creature is attacking an opponent that is being flanked by an ally, they both attack with advantage.
(It can also open and close doors as part of its movement

)
Boosting abilities
These are abilities that elevate the creature to the level of a boss or mini boss, by making them tougher to kill.
Meatshield: The creature has double its normal hitpoints and advantage on all saves.
Blooddrinker: This creature drains blood with bite attacks. Any damage this creature deals with bite attacks, it also converts to healing for itself.
Elemental shield: At will as a supernatural ability, the creature can activate or deactive an elemental shield that affects all other creatures who touch it.
Final form: When the creature is below half its maximum hitpoints, it transforms into another creature and heals back to full health. An animal could for example transform into a dire version of its type. Or a humanoid could transform into some undead or demon.