Games like Overboard!
Games like Overboard! include Her Story, No Case Should Remain Unsolved, Storyteller, The Wolf Among Us, and Murders on the Yangtze River. We matched them by the tags players give Overboard! on Steam (Adventure, Interactive Fiction, Detective, Puzzle, and Choose Your Own Adventure): closest matches first, and among equally close ones the better-known games.

Her Story
Shared: Interactive Fiction · Detective · Choose Your Own Adventure

No Case Should Remain Unsolved
Shared: Interactive Fiction · Puzzle · Adventure

Storyteller
Shared: Interactive Fiction · Puzzle · Adventure

The Wolf Among Us
Shared: Adventure · Detective · Choose Your Own Adventure

Murders on the Yangtze River
Shared: Adventure · Detective · Puzzle

Pentiment
Shared: Adventure · Interactive Fiction · Hand-drawn

The Mermaid Mask
Shared: Adventure · Detective · Interactive Fiction

7 Days to End with You
Shared: Puzzle · Choose Your Own Adventure · Interactive Fiction

The Great Ace Attorney Chronicles
Shared: Adventure · Detective · Choose Your Own Adventure

Kindergarten 3
Shared: Puzzle · Choose Your Own Adventure · Interactive Fiction

Endless Monday: Dreams and Deadlines
Shared: Interactive Fiction · Choose Your Own Adventure · Hand-drawn

The Life and Suffering of Sir Brante
Shared: Interactive Fiction · Choose Your Own Adventure · Choices Matter

Suzerain
Shared: Interactive Fiction · Choose Your Own Adventure · Choices Matter

Refind Self: The Personality Test Game
Shared: Interactive Fiction · Adventure · Female Protagonist

Sanfu
Shared: Adventure · Puzzle · Hand-drawn

Roadwarden
Shared: Adventure · Interactive Fiction · Choose Your Own Adventure

Phoenix Wright: Ace Attorney Trilogy
Shared: Detective · Adventure · Puzzle

Return of the Obra Dinn
Shared: Detective · Puzzle · Adventure

Who's Lila?
Shared: Detective · Choose Your Own Adventure · Interactive Fiction

Danganronpa 2: Goodbye Despair
Shared: Detective · Adventure · Puzzle

The Henry Stickmin Collection
Shared: Choose Your Own Adventure · Choices Matter · Comedy

Breakout 13
Shared: Interactive Fiction · Choose Your Own Adventure · Puzzle

Slay the Princess — The Pristine Cut
Shared: Choose Your Own Adventure · Choices Matter · Hand-drawn

Confidential Killings - A Detective Game
Shared: Adventure · Detective · Puzzle