Rose-the-Cat was a cat the Tenth Doctor adopted after Rose Tyler was trapped in Pete's World. He decided that Rose was the perfect name for the cat. Rose, K9, and the Doctor lived together without any other long term companions.
Rose would often try to help the Doctor cope with the loss of his former love, through various means. Most to all of these failed. (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.