In D&D 3.5 there was a way to change type, like Animal, into a subtype, like Magic Beast (Augmented Animal)
A creature receives this subtype whenever something happens to change its original type. Some creatures (those with an inherited template) are born with this subtype; others acquire it when they take on an acquired template. The augmented subtype is always paired with the creature’s original type. A creature with the augmented subtype usually has the traits of its current type, but the features of its original type.
I would want to homebrew some monsters and creatures for 5e, based on already existing ones. I would like to do it in a way that would change their type, but they would actually be an augmented versions of the originals, so connection to their original type should not be lost.
Is there a canonical way to do it in the 5e?
General rule from a sourcebook would be great, but if there isn't one (and I'm inclined to believe there isn't as I couldn't find it) then published 1st party monsters in sourcebooks, monster manuals or campaign settings books would suffice.