Eldritch knight dual wield: do I get multiple attacks on my bonus action?

Question

I have a level 11 Eldritch Knight with two weapon fighting.

The rules say I have 3 attacks per action.

The rules say when ever I make an attack action with my main hand I can make a bonus attack action with my offhand.

Does that mean I get 3 attacks on my off hand as well?

Answer 1

No; what the rules actually say is one bonus action per turn

We will frame this answer using the action economy as written in Chapter 9. {my italics and bolding throughout}

Your Turn
On your turn, you can move a distance up to your speed and take one action.

As you state, you will take the Attack action (rather than perhaps the Dash, Disengage, or Dodge action)

Bonus Actions
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available. You choose when to take a bonus action during your turn...

You want your bonus action to be the one for two weapon fighting.

Two-Weapon Fighting (Chapter 9)

When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

But since you have this fighting style (Chapter 3) ...

Two-Weapon Fighting. When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.

... you do apply your damage bonus.

The Action is attack; a Fighter 11 gets two extra attacks when you make that attack as an action. A Barbarian 11 would only get one extra attack.

• Extra Attack is a class feature that adds attack(s) to the generic attack action. You are not taking multiple actions; you are taking one action, attack, but you get to roll for more chances for making an effective attack that does damage. A wizard could not do this. (Wrong class).

Attack (Ch 9)

The most common action to take in combat is the Attack action, whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists. With this action, you make one melee or ranged attack.
{snip}
Certain features, such as the Extra Attack feature of the fighter, allow you to make more than one attack with this action.

An Action is a different thing from a bonus action. (Yes, that can be confusing) Here is how bonus actions work - in your turn, after you take your action, or before, you get to take one bonus action. From the CH 9 two weapon fighting rule ...

you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.

A is singular, and that attack is not the same as the Attack (Action) since it is a bonus action.

So what happens is this:
You choose to make the Attack action, so you attack and add two extra attacks for your high level - total of three attack rolls for this turn's attack Action.
You can add one bonus action attack with the other weapon - total of four for this turn.

Note that "offhand" isn't addressed in this edition of the game: that term is a carry over from earlier editions.

Answer 2

RAW, no.

PHB pg189

You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.

Specific over general. The rules state that you receive your movement, one action, one bonus action, and one reaction .

If a specific rule contraddicts a general rule, the specific rule wins.

The multiattacks are an example of a specific rule breaking the general rule outlined in the Player's Hamdbook. Furthermore, the specific rule is only mentioning the Attack Action. There is no wording to assume a further inclusion of the Bonus Action as well.