Originally born on Earth, Jake Carstairs and his twin sister Vienna moved to colony planet Chelsea 426, which orbited Saturn. His parents ran a hotel there and they assigned chores to their children. Jake often dreamed of flying into space one day. When he was fourteen he met the Tenth Doctor during the Rutan invasion of Chelsea 426. He, the Doctor, Vienna, and his other Bess Carstairs went to the opening presentation of the flower show there. His mother was affected when ProfessorWilberforce activated a plant which put her under the control of the Rutan Host. He and his sister were evacuated with the Doctor. They [statement unclear]in the TARDIS, along with a stranger known as the Major. He later stopped the Sontarans from destroying the Earth. After the invasion was stopped, his mother was freed from the Rutans and he was not permitted to travel with the Doctor. However the Doctor later reassured him that when he was older he would see the universe as a starship pilot. (PROSE: The Taking of Chelsea 426)
Multi-adventures reference the rare instance when a companion is shown or stated to have multiple adventures with the Doctor but only appears in a single story.
If a medium is not mentioned, then this incarnation did not have companions who were original to that medium; it does not mean that this Doctor failed to appear in that medium.