A model of K9 lived with the Tenth Doctor in the TARDIS. K9 joined the TARDIS team while Rose Tyler was still on-board, but the robot would initially spend most of his time within the TARDIS, rarely mentioned or seen. K9 only began to actively join adventures after the Doctor adopted a cat, whom he named after Rose. The two did not get along.
K9 travelled with the Doctor during his adventures with Rose Tyler. Rose and the Doctor once considered purchasing a cat, but decided that K9 was enough for the team. (COMIC: Untitled)
After the departure of Rose from the team, the Doctor would decide to purchase a cat, just as Rose had suggested. K9 and Rose did not get along, and fought within the TARDIS on several occasions. (COMIC: A Rose by Any Other Name)
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.