The intermediate-energy $R$-matrix approach (IERM) has been developed as a first step towards representing a double-electron continua within a general multielectron $R$-matrix code. Using this method, we study photo-double-ionization of the ground states of the He and Be isoelectronic sequences and show excellent agreement with other theoretical and experimental results. We confirm scaling relations for the photo-double-ionization cross section along the He isoelectronic sequence and suggest a scaling relation, which takes into account the screening effect of the $1s$ electrons, for the photo-double-ionization cross section for Be-like ions. We also examine trends in the ratio of double to single ionization.