Aubertide

The Aubertides were a race of shapeshifters native to Aubris. They could assume the appearance of anything they ate. Once every one hundred years, the Aubertide Queen would lay eggs and the Aubertide King would fertilise them in the ground. Individual Aubertides could reproduce asexually via buds on their backs, but could only do so five times.

One Aubertide family followed the Seventh Doctor to Earth in 1914 in an attempt to gain his biodata and thus his regenerative abilities, but they were all killed or captured. (PROSE: Human Nature)

All these events were one iteration of a "story" which played out many times, each time differently. In another iteration of the story, the Tenth Doctor was pursued by the Family of Blood, who filled the same role as the Aubertides. (WC: Shadow of a Doubt)