I'm not sure what sage mode is, but you level up the heart bar by first building her trust - giving milk, skinship, and chatting (gives red heart). Then, once you have a full red heart, you increase her lust to 100%, turning it into a fully leveled purple heart.
More hearts = more events, choices, and relationship progression.
You can also buff trust gains by cooking imouto a meat dish.
Edit: Remove sage mode by equipping Girl's Smile (Received by finishing second promise).