Q414 Is it possible for a character with both the Dueling and Two-Weapon Fighting fighting styles (for instance, a level 10 Champion Fighter) to benefit from both in the same turn by attacking with a one-handed light weapon while not holding any other weapons, and then drawing another light weapon and attacking with it?

As a corollary, would that character be able to repeat this process every turn by dropping the second weapon at the start of the next turn, and either picking up the dropped weapon on the next turn or drawing a new one? (Imagine a Fighter wearing a belt with ten daggers in it.)

Relevant sections of relevant rules (no page numbers because I'm using SRD):
  • 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.
  • Two-Weapon Fighting (combat mechanic): 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.
  • Two-Weapon Fighting (fighting style): When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.

This has probably already been asked before, and I have my own idea of how it should work, but it recently came to my attention again in the process of designing a little homebrew somethin'-somethin'.