Hmm throwing in some finished games heavily focused on 1 or 2 LIs, although they may have more:
Retrieving The Past - 3 LIs. Has a "superpower" component to the story that I personally dislike, but the interaction between characters makes up for it.
Leap of Faith - There's one main LI, although there are maybe 3 or 4 more. Deals with difficult themes and tugs at your heart strings, but that brings you even closer to the characters.
Alexandra;
Haley's Story;
Avalon;
Life with Mary - Paired this 4 together because they are heavily focused on only one LI, fully fleshing out the relationships.
Melody - 4 or 5 possible LIs, mostly focused on one of them - the one whose name is the game title. Simple wholesome story.
Acting Lessons - Good game focused on mainly 2 LIs. It has a VERY controversial creative decision at the very end, but it's still a good game.