Tenchi Muyo! Hasegawa novels
The series of 13 novels was written by Naoko Hasegawa, continuing from the first OAV series, and which included the story adapted into Tenchi movie 2.
The True Tenchi novels are already licensed by Seven Seas, but the Hasegawa novels don't seem to be licensed by anyone.
This is of course a series with an existing anime.
Yes please. Still a Tenchi fan after all these years.