A Whisker Away

You may know this one as Nakitai Watashi wa Neko wo Kaburu; that's A Whisker Away under its other release name. It's a movie out of Studio Colorido. The run is complete — no gaps waiting on new episodes.

On the shelf it sits under Drama, Fantasy, and Romance — worth knowing if you're comparing drama anime specifically. If A Whisker Away works for you, A Silent Voice and Your Name. are close matches — see the full related list below.