A considerable amount of it between Winn and Superman, with the former turning into a Squeeing fanboy when he gets to meet him.
Also between Winn and Mon-El as they both go out for drinks and become instant buddies.
Also also, Winn and James (seeing a pattern here), especially in season 2 when James becomes Guardian and they spend their nights together fighting crime.
Kara once admitted that even she wanted to date Lucy Lane after she got to know her as Jimmy's ex-girlfriend for the first time.
Kara and Alex may be adopted sisters but they are rather close for that.
Cat Grant appears to be playing the role of Lois Lane to Supergirl's Superman. She's dismissive towards Kara Danvers and caustic about Supergirl, but has been shown to have a soft spot for both including several Hypocritical Heartwarming moments. Her interview with Supergirl mirrors Lois Lane's interview with Superman in the first film, minus the romantic flying scene. She is also the first person to figure out Supergirl's Secret Identity on her own much like Lois Lane in Superman II.
Kara and Lena Luthor quickly pick up a very Superman/Lois vibe once Kara becomes a reporter and uses Lena as her primary source. It also helps that Lena instructed her secretary that Kara is permitted to drop by LuthorCorp whenever she wants.
Later there is Lena asking Kara to come to her party and it looks like she is asking her on a date. Lena also tells Kara she's Lena's "only friend" and later shows up at Kara's apartment uninvited. In addition, Lena's reaction to Alex's presence could be interpreted as jealousy that Kara had another "friend."
In "Luthors," Lena and Kara's friendship is put to the test. Kara is the only one who wants to find the good in Lena, even when evidence implicates the latter of conspiring with her mother. Lena is obviously touched when Supergirl tells her how Kara believes in her innocence. Towards the end of the episode, Lena is vindicated and she says to Kara "I've never had friends like you before... I've never had family like you before."
In "Exodus", Lena is pushed off her balcony and Kara rescues her, flying up while carrying Lena bridal-style. It's reminiscent of the way her cousin carried Lois Lane.
In "Ace Reporter" Kara hears that Lena is at dinner with her ex-boyfriend and runs off to crash it, which Mon-El even points out makes her seem like a Stalker with a Crush. They end the episode with a tender embrace after the ex's death, with Kara promising that Lena will always have her. Lena, meanwhile, flatteringly describes Kara as "the best reporter in National City." (Which causes Kara to become bashful in a manner reminiscent of her early interactions with Jimmy.)
In "Resist", Kara is very distraught that Mon-El and Lena are trapped on the Daxamite ship which the president has ordered destroyed.
Kara: But all I think about is the fact that two people I love are trapped on that ship and if we destroy it, then they're destroyed, too, and that will break my heart.
The entire last third of Season 3 can easily come off as a messy love triangle between Kara, Lena, and Sam. In particular, Supergirl trying desperately to repair her relationship with Lena after a breach of trust, and Lena having none of it, point-blank telling Supergirl that they aren't friends and don't need to be friends, because Lena has friends of her own. Supergirl (and Kara, one of those friends Lena was talking about) is very hurt by this.
Kara's confession scene in the season five premiere can come off as a love confession. Moreover, it is worth noting that Kara, arguably, never got this emotional with Jimmy or Mon-El. Furthermore, when she faced the prospect of dying while fighting Reign, Kara did not express any fear. However, when confessing her secret to Lena she voices the fact that the possibility of losing Lena frightens her.
Furthermore, when Kara gifts Lena a signal watch at the end of the premiere, one could interpret the scene as a proposal of sorts because the Girl of Steel is reifying her trust in Lena via the gift.
In "Blurred Lines," Kara goes to Europe to retrieve breakfast for Lena after telling Nia that food may be Brainy's "language of love" a few episodes prior.
In addition, Kara willingly breaks into Fort Summit for Lena to retrieve Lex's journals in an effort to comfort Lena and help her "heal." After she gets the journals, she heads to Lena's apartment and stares at her for a bit before smiling softy when the Luthor notices her.
The cherry on top of all of this is the arguably romantic music that plays over this scene and the parallels between Kara and Lena's scene and Kelly and Alex's. (With the song being Freya Ridings' 2019 single "You Mean the World to Me.")
In Tremors," Lena finally reveals that shes been playing Supergirl all season and confronts Kara about lying throughout their relationship. The fact that theyre both reduced to tears and Lenas absolute anguish at being betrayed by Supergirl definitely comes off like a lovers quarrel.
In the next episode, Kara foils Lena's plans but Lena escapes justice. Alex and Kara talk about how Kara will fight to save Lena, even at great cost to the world. This is followed by a match cut of both Lena and Kara looking at the same picture of the two of them together with great sadness.
Moreover, the song played over this scene (Olive James' 2020 single "Head Above Water") arguably held romantic connotations. This seemed to be somewhat fortified when, during the Batwoman episode "Through the Looking-Glass," Kate kisses Julia Pennyworth on a balcony after Julia assures Kate that she is a good person after the latter murdered Cartwright.
Imra seems very starstruck and infatuated by Kara.