As of Generation 9, the only moves that can "drastically" raise a stat are:
Cotton Guard: +3 Defense
Fell Stinger: +3 Attack if it KOs a Pokemon
Tail Glow: +3 Special Attack
Z-Splash: +3 Attack
There's also the X "stat" 3 in-game items, like the X Attack 3, which boost a stat by 3 stages; however, that cannot be used in online battles. (And then there's X "stat" 6, which supposedly immensely boosts a stat, but that's not a drastic boost so I'm only mentioning it.)
However, with the ability Simple and a move that "sharply" raises a stat, you can change a move that's supposed to give a +2 boost into one that gives +4. For example, Nasty Plot sharply raises Special Attack (+2 Special Attack), but with the ability Simple, that will change to +4 Special Attack and will say that the move "drastically" raised Special Attack.
Here are all the moves that can achieve this (with Simple, of course):
(if the move is directed towards an a target Pokemon, that Pokemon that gets their stat boosted must have Simple, not the user)
Acid Armor: +2 Defense
Acupressure: +2 to a random stat (excluding accuracy and evasion)
Agility: +2 Speed
Amnesia: +2 Special Defense
Autotomize: +2 Speed, user's weight is halved (becomes nimble)
Barrier: +2 Defense
Decorate: +2 Attack and Special Attack to target Pokemon
Diamond Storm: Chance to provide +2 Defense after attack
Fillet Away +2 Attack, Special Attack, and Speed, but loses half health
Geomancy: +2 Special Attack, Special Defense, and Speed after a charging turn
Growth: +1 Attack and Special Attack, +2 if under Sun
Minimize: +2 Evasion
Nasty Plot: +2 Special Attack
Rock Polish: +2 Speed
Shell Smash: +2 Attack, Special Attack, and Speed, but -1 Defense and Special Defense
Shelter: +2 Defense
Shift Gear: +2 Speed and +1 Attack
Spicy Extract: +2 Attack and -2 Defense to target Pokemon
Stuff Cheeks: +2 Defense, in addition to using the user's held berry
Swagger: +2 Attack to target Pokemon and confuses it
Swords Dance: +2 Attack
Z-Ally Switch: +2 Speed
Z-Aromatic Mist: +2 Special Defense
Z-Bestow: +2 Speed
Z-Captivate: +2 Special Defense
Z-Heal Block: +2 Special Attack
Z-Imprison: +2 Special Defense
Z-Last Resort from Eevee (Extreme Evoboost): +2 Attack, Defense, Special Attack, Special Defense, and Speed
Z-Magic Coat: +2 Special Defense
Z-Me First: +2 Speed, then calls a Z-Move
Z-Mirror Move: +2 Attack, then calls a Z-Move
Z-Powder: +2 Special Defense
Z-Psycho Shift: +2 Special Attack
Z-Recycle: +2 Speed
Z-Snatch: +2 Speed
Z-Switcheroo: +2 Speed
Z-Trick: +2 Speed
Additionally, here are all the moves that can drastically lower a stat (again, with Simple):
(if the move is directed towards an a target Pokemon, that Pokemon that gets their stat boosted must have Simple, not the user)
Acid Spray: -2 Special Defense to target Pokemon
Captivate: -2 Special Attack to all adjacent opposing Pokemon if of opposite gender
Charm: -2 Attack to opposing Pokemon
Draco Meteor: -2 Special Attack after attack
Eerie Impulse: -2 Special Attack to target Pokemon
Fake Tears: -2 Special Defense to target Pokemon
Feather Dance: -2 Attack to target Pokemon
Fleur Cannon -2 Special Attack after attack
G-Max Foam Burst: -2 Speed to all opposing Pokemon after attack
Leaf Storm: -2 Special Attack after attack
Lumina Crash: -2 Special Defense to target Pokemon after attack
Memento: -2 Attack and Special Attack to target Pokemon, user faints
Metal Sound: -2 Special Defense to target Pokemon
Obstruct: -2 Defense to any Pokemon making contact, in addition to protecting from damaging attacks
Overheat: -2 Special Attack after attack
Psycho Boost: -2 Special Attack after attack
Scary Face: -2 Speed to target Pokemon
Screech: -2 Defense to target Pokemon
Seed Flare: Chance to -2 Special Defense to target Pokemon after attack
Spicy Extract: -2 Defense and +2 Attack to target Pokemon
Spin Out: -2 Speed after attack
String Shot: -2 Speed to target Pokemon
Sweet Scent: -2 Evasion to foe(s) Pokemon
There's also the X "stat" 2 items, which now boost a stat by 4 stages and thus drastically boosts a stat.
Finally, a few held items can drastically boost a stat when activated.
Blunder Policy: +2 Speed if move misses because of accuracy
Starf Berry: +2 to a random stat (excluding accuracy and evasion) when HP is 25% or lower
Weakness Policy: +2 Attack and Special Attack if hit by a super effective move