We present an extension of the renormalisation procedure based on the R-operation in $D$ dimensions at two-loop level, in which the numerators of all Feynman diagrams can be constructed in four dimensions, and the rational terms stemming from the interplay of $(D-4)$-dimensional numerator parts and UV poles are fully reconstructed from a finite set of universal local counterterms.
This represents an extension of the concept of rational terms of type $R_2$ to two loops. We provide a general method to compute one and two-loop rational counterterms from massive one-scale tadpole integrals.
Finally, we present the full set of rational counterterms of UV origin for QED up to two-loop order.