Macroevolution, as typically understood, consists of three grand claims:
First, that all organisms share common ancestry, i.e., all species, whether extant or extinct, branched out from one or a few ancestors in a distant past. This also means that all living beings are connected by the process of natural biological generation.
Second, that the transformation of one species into another species is possible by means of natural generation. This means that an individual or a population of one type of organism can (and in fact will) change into an individual or population of a completely different type of organism, given enough time and other natural conditions (e.g., including mutations and selection pressure).
Third, that the changes that have produced all the diversity of life were natural, i.e., happened thanks to the properties and laws inherently present in nature. No supernatural power worked in this process.
All the three claims are an object of the ongoing controversy. Consequently, the problem of compatibility of Thomistic philosophy with biological macroevolution boils down to three questions: Is Thomism compatible with universal common ancestry? Is Thomism compatible with the transformation of species? Can species be produced naturally?