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I think the best way to attenuate the blandness in your superhuman character is by dropping the superficiality of invulnerability. Your protagonist might be an epitome of impeccability but what you...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/4900 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
I think the best way to attenuate the blandness in your superhuman character is by dropping the superficiality of invulnerability. Your protagonist might be an epitome of impeccability but what you have to keep in mind is that his challenges are equally overwhelming. The negative character that he is supposed to overcome or deal with should be having equal and opposite powers of similar amplitude and should be overall equally resourceful. That way no one is an underdog and what we have is a battle of equals, which is interesting in a way. Now once your plot has these elements in place what you need is a personal life attached to these characters, which is going to spin enough controversy to keep the reader interested. Now there are various ways of depicting an impaired personal life. The most usual way to go about it is to create a character from the opposite sex who has a history with the protagonist, and maybe seduces the protagonist or gets him/her in a trance by so much as looking at her/him, but unfortunately plays for the opposite team. This sounds exaggerated but you have to decide on the meticulous details depending on what kind of picture you're interested in painting/at what pace you want your novel to move/in which era of history does the chaos breed, you know basically the 'theme'. Another way of doing it is by showing him having an emotionally malnourished childhood and the fact that he went into drugs and is unable to quit so needs rehabs and without a regular visit to a rehab or without refueling himself periodically with a certain chemical he is no more than a freak dancing to the music of oppression. Use him like a lock with a rusty key that needs to be lubricated for the lock-key system to work properly and give the lubricant to his opponent and watch the story take shape...