A short story, "Moving On", in Virgin Publishing's Decalog 3: Consequences anthology and the Big Finish Productions-produced Sarah Jane Smith audio play Mirror, Signal, Manoeuvre (both written by Peter Anghelides) indicate that K9 Mark III broke down and Sarah was unable to repair it as the replacement circuits would not be invented for several centuries.
When the Tenth Doctor created K9 Mark IV to replace K9 Mark III, he added a shiny metallic blue paint job and other improvements, including an omniflexible hyperlink facility. (TV: School Reunion) Later, though, K9 reverted to his old dark green colour. (TV: Invasion of the Bane) In battling Mr Smith (and following the battle) K9 displayed a teleport facility and a laser weapon similar to the previous K9s'. (TV: The Lost Boy)
Jealous, Possessive by Paul Magrs, the "Scorpio" story in Big Finish's anthology Short Trips: Zodiac features K9 Mark I and Mark II relaying their exploits to each other, and their veiled put-downs to each other reveal that each considers the other to be the "inferior" version. This attitude is also occasionally hinted at in the way the two units refer to each other in the Gallifrey audio series.