Solo Boss fights
Fighting an opponent one on one in a battle of intelligence can be a very dramatic turn of events.
Basics
(Primary difference between this and dueling is that a solo boss fight, as well as general fights, require the user to pay just as much attention to their surroundings as their opponent while in dueling you just have to pay attention to the opponent)
Any party members left out of the boss will take one of the following rolls if they have a substantial role play to contribute with the character. (In the case of lovers it might be a kiss. In the case of friends it might be heartfelt words. In the case of family it might be a hug. For brothers in arms it might be the sharing of equipment. Etc.). The players whose characters are not participating in the fight will then roll the chosen dice when applicable.
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Roll a 1d4 and add it to a specific weapon attack roll, ability check, or saving throw. (It can only be one type of weapon, ability or saving throw roll determined before the combat by the player doing the roll) (d6 for non combat characters) (up to 2 per round)
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The player can roll an inspiration die once per round for any applicable roll though it can’t be a roll that has already been altered or will be altered by another player's d4. (d8 for normal. d10 for non combat characters.) (1 die every 2 rounds)
Alternatively, this could be applied to a solo mission, like the rogue entering a fortress to take out the leader before attacking.