Platonic (2014)

The plot isn't similar at all, but for some reason both of the male leads give off a similar feeling. If you appreciated Platonic, I think you'd also like the much slower paced movie.

Both are dramas about someone needing an organ transplant for a family member. They meet someone with a terminal illness who is willing to donate. They must get married for the transplant to be legal but eventually end up falling in love.

In Nagareboshi, the male lead marries the female lead so that she will be a donor for his sister while in Platonic, the female lead marries the male lead so that he will be a donor for her daughter.

Everything else is quite different since Platonic takes a darker tone while Nagareboshi is lighter in comparison.

Terminal illness, family, and a great love story. Both feature Domoto Tsuyoshi as the love interest, and the surrounding cast is similarly wonderful. If you liked him in Summer Snow, he pulls off the same role wonderfully in Platonic.