There is the vague plan of a sequel someday, but nothing of the like has been announced yet. Due to popular demand, some more content will be added to House Chores (like the upcoming v1.3 mentioned in my FAQ).
Currently there is a spinoff prequel in development called "Room Service". It focuses on different characters from the same neighbourhood. This game is in very early stages of development though. The developer stated in their recent "Progress Update" Patreon post that they will resume regular updates for that game once the new content for House chores has been added.