Or, have I been doing it wrong? I'm looking at 'You can't take a Fighting Style option more than once, even if you later get to choose again.' (PHB p.91)
Fighting classes often give combat styles early on. Are they cumulative, or do they replace previous styles? If they are cumulative, what if they weren't? Combat styles are very powerful and getting a second combat style is one of the defining features of the higher-level Champion Fighter.
As others have said, you can take
different styles when multiclass or 11th-level champion. However, our group disagrees about them being "very powerful" so we house-ruled extra features:
Archery
You gain a +2 bonus to attack rolls you make with ranged weapons.
If you have made an attack with a ranged weapon, you can use your bonus action to make another ranged weapon attack of the same type (missile or thrown) . You cannot use this feature with a weapon with the Loading property.
Defense
While you are wearing armor, you gain a +1 bonus to your armor class.
You can use your reaction to half the damage from one attack. You can use this feature after the attack is rolled, but before damage is determined.
Dueling
When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon and any attempts to disarm your weapon are with disadvantage.
After you have made an attack with your melee weapon, you can use your bonus action to make a second attack with the same weapon.
Great Weapon Fighting
You gain a +1 to damage when wielding a weapon with both hands. When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2. The weapon must have the heavy or versatile property for you to gain this benefit.
You can use your bonus action to grant yourself a +1 bonus to your AC until the start of your next turn.
Protection
While wielding a shield, you gain a +1 bonus to your AC. When a creature you can see attacks
a target that is within 5 feet of you, you can use your reaction to impose disadvantage on the attack roll.
Two-Weapon Fighting
When you engage in two-weapon fighting, you add your Strength ability modifier to the damage of both weapons.
Fighting with two weapons does not cost your bonus action.
So all the new features require either a bonus action or reaction, except TWF which removes the need for a bonus action.