In "The Survivor" an episode of the kind of sort of semi-canon Star Trek: The Animated Series an multi tenticled Vendorian was encountered. Vendorians can take the shape of other life forms, and this particular one even turned himself into a functioning machine while that machine was desperately needed!
KIRK: There used to be only two examining tables in this room. Now there are three.
SPOCK: I just realised that.
KIRK: This is a vial of Orientine acid, Winston. It will burn through almost anything but this crystal. If you've never seen it work, I'll demonstrate on you.
(The table transforms into the alien)
MCCOY: I saw that, but I don't believe it.
SPOCK: A Vendorian, Doctor. Their planet is quarantined, and few people ever do see them. Their ability to rearrange their molecular structure into anything with the same general size and mass and their practise of deceit as a way of life puts them off limits.
KIRK: Mister Spock, get a security team down here on the double.
KIRK: Good work, Mister Scott. That deflector shield went up just in time.
SCOTT: But sir, I haven't finished repairing the shield. I told you it'll take hours, and it will.
KIRK: Then what was? Winston.
SPOCK: It is not outside the realm of probability. If he could rearrange his own atoms to become an examination table, one would have to assume he could become a deflector shield.
When Garth of Izar was severely wounded near Antos IV, the Antosians taught him the process of cellular regeneration to heal himself, and Garth later used it to change his shape and impersonate other beings (Star Trek: The Original Series "Whom Gods Destroy").
KIRK: How does he manage to change form at will?
CORY: The people of Antos taught him the techniques of cellular metamorphosis to restore the destroyed parts of his body. By himself, he later learned to use the technique to recreate himself into any form he wished. The first time we knew about it was when a guard, seeing what he thought was me in Garth's cell, released him.
So Captain Kirk should have kept an open mind and not been certain that Cameloids were a myth until Star Trek VI: The Undiscovered Country.
MARTIA: I'm a chameloid.
KIRK: I've heard about you. 'Shapeshifters', I thought you were mythical.
So that might (depending on various factors such as the canon status of TAS and whether cellular regeneration is innate to all Antosians) possibly make as many as three other canonical shape shifting biological (non energy beings) species in Star Trek before the changelings in Star Trek: Deep Space Nine!