I looked through the Uesp bestiary, to find several choices for the next possible mount which one do you want it to be?
Unicorns are at the top of the list because like the Indirk, are magical creatures that can rather easily adapt to the current system, instead of feathers it could be unicorn horns that morphs them.
What is a Unicorn, in Tes they are considered creatures of good and light going by lore introduced in Daggerfall. Eso has them being creatures native to the Hunting Grounds and are prey to his hunters. So they are associated with Hircine and are a creature native to his realm of Oblivion. Hircine brings them to Tamriel for mortals to hunt which ended up causing them to became basically extinct with the exception of one in the third/forth era.
https://en.uesp.net/wiki/Lore:Unicorn
Here is information on
https://en.uesp.net/wiki/Lore:Wamasu#References
Here is some information on the Welwa from uesp beastary.
According to tapestries in the Crystal Tower, the early Aldmeri settlers of the Summerset Isles encountered welwa, depicted as strange, holy ravagers, and saviors of the land.[1] Led by Torinaan, the Aldmer of Auridon drove them back using ancestral magics,[2] and eventually the welwa of Summerset were driven to extinction.[3] In Yokuda they were considered myths, and described in their ancient texts as having "the jaws of a bear, and the charging strength of a boar".[4]
Welwa continued to inhabit the wilds of Craglorn on mainland Tamriel. They are often domesticated and armored by the Iron Orcs of the region, who use them as war beasts. In the Second Era, the Sapiarchs of the Crystal Tower reintroduced welwa to Summerset Isle by bringing in mated pairs from Craglorn. These welwa quickly spread across the wilderness of Summerset, although many inhabitants of the Isle were displeased with their reintroduction.[3]
The Salamander isn't like a real life one , they also have intense elemental magic and because of the uniqueness of them in Elder Scrolls they are listed as a potential choice.
Echatere are Orcish Yaks like animals that have a unique insect like body, They are basically mammalian centipedes with antlers.
Elytra are native to the Shivering isles and have their own unique properties. Unlikely it would ever be a thing but I listed them anyways.
https://en.uesp.net/wiki/Lore:Elytra
Chaurus are native to black reach, they are used by the Falmer, they are bug like creatures that are dangerous but are domesticated by the Falmer.
Mammoth's are listed just because they would make a great mount. They would be great for an event mount where they can give several variations to them They would make great stand alone mounts without any form of morphing system for them. Maybe gather components allowed to tame them for use as a mount.