Iinazuke wa Imouto-sama!

Shun lives alone with his sister Yuna after their father remarries. Yuna acts harshly to Shun and often yells at him for the slightest mistakes. Suddenly Haruka arrives unannounced and claims to be Shun and Yuna's new sister. Since she's Shun's new sister she believes that must mean they love each other and if they love each other that must mean they're engaged to be married and if they're engaged to be married that must mean they should do ecchi things together.

Yuna fights back for her brother and announces that she won't give Shun up to Haruka or anyone! Haruka then concludes that Yuna must love Shun too and if she loves Shun too that must mean they're engaged to be married as well and if they're engaged to be married as well that must mean they should all do ecchi things together!

(Source: VNDB)