Comparative genomics supports macroevolution in all sorts of ways. For one, species on particular branches of life share not only functional elements (which could be explained by a common designer, just as a shared spine could be), but nonfunctional ones as well. For example, all apes and monkeys share an inability to make their own vitamin C because they lack a functioning version of a particular gene. The gene is still there in all of their genomes, in recognizably the same place, but it's badly broken, and often broken in the same ways. Some other species (e.g. guinea pigs) have also lost functional versions of the same gene, but they're broken in different ways. This makes sense assuming common descent is correct: the primate share the broken gene because they've all inherited it from a common ancestor in which it first broke.
There are hundreds of thousands of other examples -- other broken genes, nonfunctioning, malformed copies of working genes, retroviruses that have inserted themselves into genomes, other transposable elements that have done the same -- all consistently reproducing an almost identical tree-like structure of shared features.
And then there are other indications of common descent that rely not on similarities but on differences. I've explained one of these at length here:
Testing Common Ancestry: It’s All About the Mutations - Article - BioLogos