Harmony Shoal

The Shoal of the Winter Harmony were a race that moved from planet to planet, taking over the bodies of the original population. (TV: The Return of Doctor Mysterio) At some point they were conquered by King Hydroflax, whom they revered fanatically. (TV: The Husbands of River Song)

Biology
The Doctor described the Shoal as "multi-nucleated organisms functioning as an infinitely adaptable, independently functioning peripatetic central nervous system". Physically, the Shoal resembled disembodied brains with eyes. (TV: The Return of Doctor Mysterio)

To move and interact with their environment, the Shoal appropriated the bodies of humanoids by removing the original brain and emplacing themselves. These "containers" gained a distinctive diagonal slash that split the head in two; the Shoal could separate the halves at will and hide objects inside. The internal structure of these individuals became blue and slimy. (TV: The Return of Doctor Mysterio)

History
The Shoal attempted to invade Earth in 2016, using the business Harmony Shoal as a front. They planned to crash a spaceship into New York City, destroying everything but the Harmony Shoal building (which had been constructed in such a way that it was able to survive atomic bombs). This would cause authority figures and world leaders to take refuge inside the Harmony Shoal buildings, which had been placed in every capital city on Earth. The Shoal planned to replace their brains and then colonize Earth. They were defeated by the Twelfth Doctor and Grant Gordon, and subsequently apprehended by UNIT. (TV: The Return of Doctor Mysterio)

The Shoal intended to buy the Halassi Androvar from River Song to honour Hydroflax, not knowing that the diamond was inside Hydroflax's head. Scratch and other members of the Shoal met River aboard the Harmony and Redemption, though the sale was derailed after they found out where the diamond was. (TV: The Husbands of River Song)

Behind the scenes

 * Their design of disembodied brains with eyes in a jar is similar to the Morpho, though they are not stated to be related.
 * Their ability to wear a body suit by opening them through the head is similar to the Slitheen. The difference was that the Shoal opened their heads by a slight touch to the cut on their heads, as opposed to the Slitheen who open the skins by a zipper just below the hairline.