Through a comprehensive theoretical study, we demonstrate that single-molecule junctions formed from asymmetric molecules with different terminal groups can exhibit Seebeck coefficients, whose sign depends on the orientation of the molecule within the junction. Three anthracene-based molecules are studied, one of which exhibits this bi-thermoelectric behaviour, due to the presence of a thioacetate terminal group at one end and a pyridyl terminal group at the other. A pre-requisite for obtaining this behaviour is the use of junction electrodes formed from different materials. In our case, we use gold as the bottom electrode and graphene-coated gold as the top electrode. This demonstration of bi-thermoelecricity means that if molecules with alternating orientations can be deposited on a substrate, then they form a basis for boosting the thermovoltage in molecular-scale thermoelectric energy generators (TEGs).