A few games that star Luigi solve the issue in two ways. The first is by restraining Mario so that he is helpless, putting the spotlight on Luigi so that he is the only one that can rescue his brother. This is best seen in many of the Luigi's Mansion games and Mario is Missing. The other solution is to simply leave Mario out of the game so that Luigi never have to deal with his brother unintentionally hogging the spotlight, which are best seen in Dr. Luigi and Luigi's Mansion Arcade. Perhaps this would be justified when Luigi was not considered a big character back before the Gamecube was released (remember: Luigi's appearances were not very frequent back then).
However, things have changed now. In this era, Luigi is unquestionably one of the biggest Nintendo characters, up there with Mario and some say bigger than Mario. In fact, Luigi has a year named after him and how fans are more inclined to aggrandise Luigi or to more easily forgive his misfortunes, compared to how Mario's flaws are amplified, accusations are still prevalent, and his qualities downplayed.
So this brings us to the main thrust of the topic. Since Luigi is already gotten an almost major star power as Mario himself, could Mario feasibly in Luigi's game while retaining the game's title right solely to Luigi? Mario is, after all, a very inviting fellow because even though he's the star, it's not unusual for him to invite his friends to co-star alongside him, like how a few have Luigi as an equal to Mario like Super Mario Galaxy and Super Mario 3D Land. What about if the roles are reversed? Such a thinking an understandably be difficult to envision, because all this while, Mario never got to play a significant supporting role in Luigi's games, and most Luigi games only star Luigi and Luigi only, even Luigi's Mansion 3 (Gooigi is still by all accounts Luigi in a different form), so the paradigm shift might be too much for some. That's where your opinions come in!
Thank you for reading.