This is SUCH a complicated question!
It has to be a fundamental change in physiology and it has to lead to a whole bunch of organisms, not just one (like, some scientists think humans should no longer be called mammals but something else based on our intelligence, but there aren’t enough of us to call us a monumentally new clade IMO) Plus the only new thing we’ve got is large intelligence, I mean we haven’t changed our basic morphology that much
I think some sort of organism that figures out a new form of metabolism or something similar would fit the bill - like we’re endothermic organisms, but if there was a way to both maintain a constant body temp and change that temperature ourselves without much effort, that would be something. Like I get hot all the time; an organism of this kind would just be like “I don’t feel like being hot, I’m going to change my internal temp to something cooler” and then just do it
Or morphology would be a different class in general. Like if dragons had existed I wouldn’t call them reptiles cause they have SIX FREAKING LIMBS. Totally different class.
Plus the lines between organisms are so blurred. I mean frankly if we call birds a new class then most of the things we use to characterize birds apply to a whole fucking lot of dinosaurs. But not all dinosaurs are birds. All birds are dinosaurs. So do we draw the class distinction at dinosaur? But dinosaurs aren’t fundamentally different from reptiles. *head explodes*
Meanwhile, mammals actually have a lot of distinct differences from synapsids (mainly, mammary glands; it doesn’t seem like a lot of synapsids had those at least to my knowledge.) But does that make them a new class? What class do synapsids belong to? They aren’t even reptiles!
Under the traditional nomenclature codes, such as the International Code of Zoological Nomenclature and the International Code of Nomenclature for algae, fungi, and plants, taxa that are not explicitly associated with a rank cannot be formally named, because the application of a name to a taxon is based on both a type and a rank. The requirement for a rank is a major difference between traditional and phylogenetic nomenclature. It has several consequences: it limits the number of nested levels at which names can be applied; it causes the endings of names to change if a group has its rank changed, even if it has precisely the same members (i.e. the same circumscription); and it is logically inconsistent with all taxa being monophyletic.
Especially in recent decades (due to advances in phylogenetics), taxonomists have named many “nested” taxa (i.e. taxa which are contained inside other taxa). No system of nomenclature attempts to name every clade; this would be particularly difficult in traditional nomenclature since every named taxon must be given a lower rank than any named taxon in which it is nested, so the number of names that can be assigned in a nested set of taxa can be no greater than the number of generally recognized ranks. Gauthier et al. (1988) suggested that, if Reptilia is assigned its traditional rank of class, then a phylogenetic classification has to assign the rank of genus to Aves. In such a classification, all ~12,000 known species of extant and extinct birds would then have to be incorporated into this genus.
The current codes also have rules stating that names must have certain endings depending on the rank of the taxa to which they are applied. When a group has a different rank in different classifications, its name must have a different suffix.
In phylogenetic nomenclature, ranks have no bearing on the spelling of taxon names (see e.g. Gauthier (1994)and the PhyloCode). Ranks are, however, not altogether forbidden in phylogenetic nomenclature. They are merely decoupled from nomenclature: they do not influence which names can be used, which taxa are associated with which names, and which names can refer to nested taxa.
The principles of traditional rank-based nomenclature are logically incompatible with all taxa being strictly monophyletic. Every organism must belong to a genus, for example, so there would have to be a genus for every common ancestor of the mammals and the birds. For such a genus to be monophyletic, it would have to include both the class Mammalia and the class Aves. In rank-based nomenclature, however, classes must include genera, not the other way around.
It can get very messy from a phylogenetics perspective but for the basis of this question I think we should start from the original argument that these organisms would be fundamentally different in anatomy.