My go-to answer is "run it like a TV show".
Your main character is exactly that, the main character. The main character (of action/adventure shows) generally excels above the supporting cast; if she does not excel, she will eventually excel via destiny/leveling up/finding the magic comet/whatever and her story becomes the Zero to Hero / Hero's Journey plot.
Speaking of plots, pick any TV series, put aside a big chunk of time (when it happens, you'll know), and search it at
TV Tropes. You'll understand story design pretty quickly from seeing how tropes are used to build a TV cast, setting and plot.
Single-character adventures work best when they're urban-centric, but if you're comfortable having the Hero adventure with a regular team of pals with their own goals/ambitions (like, say Dragon Age, or the Final Fantasy series of video games), by all means, have your Hero brave the dungeons, kick the doors and loot the rooms - just be sure to adjust encounters appropriately.
One interesting thing I noted about the video game Dust: An Elysian Tail, is that the protagonist is actually a three-person party: The Hero (Samurai Cat), his companion (a talking, magic-using dragon/cat/thing), and his weapon (an intelligent blade containing the Soul of a Warrior). You COULD conceivably have a Warrior-Caster-Rogue relationship with a team like this without ever adding a new meat-shield to the team.