Chain shuttling copolymerisation (CSP) is a synthetic strategy allowing the one-pot, one-step formation of block copolymers. Initially developed in the frame of coordinative polymerisation of olefins and conjugated dienes, it was recently transferred to the ring-opening polymerisation of cyclic esters. In this contribution, we report six new catalytic systems able to perform the chain shuttling copolymerisation of L-lactide (L-LA) with ε-caprolactone (ε-CL) and to tune the thermal properties of the resulting copolymers. They are based on amino(bis)phenolate supported aluminium complexes bearing different pendant donorarms (Al(O2NL)OBn), L = NEt2 (2a), NBn2 (2b), Py (2c), Mor (2d)). A Mannich reaction allowed the ligands synthesis. The two new alkoxide complexes 2a and 2b were obtained by reaction of the protonated ligands with trimethylaluminium followed by benzyl alcohol in reasonable yield, as well as two already described compounds 2c and 2d. Initially assessed as catalysts for L-LA and ε-CL homopolymerisations and statistical copolymerisation, the aluminium compound bearing pyridine as a donor arm (2c) resulted in a high selectivity toward lactide. 2c together with yttrium and aluminium alkoxides, also known for their selectivity for lactide, were successfully assessed for the chain shuttling copolymerisation of L-LA with ε-CL in combination with the three other amino(bis)phenolate supported aluminium complexes that showed a higher selectivity toward ε-CL. Chain shuttling copolymerization via transalkoxylation between two different metals, Y and Al, is achieved for the first time, therefore extending the range and scope of cyclic esters CSP. Such an alteration of the nature of the catalysts allowed fine tuning of the thermal properties of the chain shuttled copolymer, as shown by a variation of the glass transition temperature (Tg) of the soft block over ca. 25 °C without changing the catalysts ratio and feed of the reaction.