male lead is female lead's emotional support as she loves/dates another guy

Try watching the original taiwanese version of The Time We Were Not In love,  waaaaaayyy better: In Time With You

Others: Dream High, Operation Proposal, Feast of the Gods, Goho's Starry Night, My Little Bride (movie), I Need Romance2, i need Romance 3, 

Not really, but still check it out: Because its the first time (though they did not end up together, he was still one hell of a supportive guy. The other guy is also a very good friend of theirs.)

Imperial Doctress is the first one that comes to mind. I Hear Your Voice fits too I think. Witch's Romance, more or less (she goes on some blind dates and her ex-fiancee shows up out of the blue at one point). The King's Woman in some respects, but maybe not really the dynamic you're looking for (he basically holds her hostage and tries / somewhat succeeds in making her fall for him / not really her emotional support). In Empress Ki, the dynamic is a bit like the King's Woman, and you could even say your criteria sort of applies to both romantic leads in different ways. 

In all of these (except maybe Empress Ki where male lead A loves her first but has to watch her marry male lead B, but later finds out she had his kid and still loves him but also male lead B knows that she loves male lead A for most of the drama, but she marries him and sort of falls for him later on - its complicated), the girl is aware that the guy has feelings for her, in most cases from very early on, but doesn't fall for him until much later even though they are still close / she relies on him for support in certain circumstances. 

Also, Healer sort of has this dynamic, except the male lead is both roles? (his undercover / clark kent persona is the emotional support guy who has to watch her have feelings for someone else and his night courrier identity is the guy she first has feelings for). 

Definitely:  Weightlifting Fairy Kim Bok Joo (Female Lead and Male Lead are childhood friends who reunite in college. ML had a childhood crush on this childhood friend, while the FM ends up falling for the ML's older brother. In the process ML (though teasing her at times) ends up supporting FM through thin and thick)

But others that might be like that (generally the girl has a crush on somebody else but ends up falling for the male lead) are ***********:

Surplus Princess

Plus Nine Boys

One More Happy Ending

Heart to Heart - Female MC suffers from a condition that makes her severely blush and as a result develops social phobia. She meets a psychiatrist who helps her overcome her phobia. (really cute drama imo) 

Flower Boy Next Door - Female MC is a recluse that lives inside her house and rarely goes outside or talks to other people. One of the neighbors helps her overcome her shyness

 Birth of a Beauty - After she found out that her husband has cheated on her, the Female MC seeks out a plastic surgeon to give her overweight former self a makeover as a part of a revenge scheme against her husband.  The surgeon becomes a partner in crime and her helping hand in this revenge scheme. 

MAJOR SPOILER ALERT for this drama (because the drama centers around the mystery of who the Female MC ends up with):  Reply 1997 - in a (k-drama) world full of Male Leads always getting the girl, this drama is famous for the Second Male Lead finally getting the Female Lead

****** Please keep in mind that it's been a while since I have seen some of these dramas so I don't remember all the details and whether what you requested rings true for all of these dramas.