After the departure of Rose from the team, the Doctor would indeed adopt 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.