Solar-assisted cooling technology has enormous potential for air-conditioning applications since both solar energy supply and cooling energy demand are well correlated. Unfortunately, market uptake of solar cooling technologies has been slow due to the high capital cost and limited design/operational experience. In the present work, different designs and operational modes for solar heating and cooling (SHC) absorption chiller systems are investigated and compared in order to identify the preferred design strategies for these systems. Three control scenarios are proposed for the solar collector loop. The first uses a constant flow pump, while the second and third control schemes employ a variable speed pump, where the solar collector (SC) set-point temperature could be either fixed or adjusted to the required demand. Series and parallel arrangements, between the auxiliary heater and the storage tank, have been examined in detail from an energy efficiency perspective. A simulation model for different system layouts is developed in the transient system simulation environment (TRNSYS, Version 17). Simulation results revealed that the total solar fraction of the plant is increased by up to 11% when a variable speed solar loop pump is used to achieve a collector set-point temperature adjusted according to the building load demand. Another significant finding of this study is that a parallel configuration for the auxiliary heater out-performs a conventional series configuration. The yearly performance of an auxiliary heater in parallel with the storage tank enhances the plant solar fraction, and the average collector efficiency, by up to 13% and 9%, respectively (as compared to the same components in series). Taken together, nearly 20% higher solar fraction (as compared to conventional designs) is possible through the control strategies and operational modes presented here without adding a substantial capital cost to the system.