In recent years, autonomous robots have proven capable of solving tasks in complex environments. In particular, robot manipulations in activities of daily living (ADL) for service robots have been in wide use. However, manipulations such as loading a dishwasher or folding laundry are difficult to automate robustly. In addition, manipulations of grasping multiple objects in domestic environments present difficulty. To perform those applications better, we developed robotic systems based on shared autonomy by combining the cognitive skills of a human operator with autonomous robot behaviors. In this work, we present techniques for integration of a shared autonomy system for assistive mobile manipulation and new strategies to support users in the domestic environment. We demonstrate that the robot can grasp multiple objects with random size at known and unknown table heights. Specifically, we developed three strategies for manipulation. From experimental results, we observed that the first strategy has the highest success rate (70% for random objects) up to 70 cm table height. Two other strategies perform better for 80 cm to 100 cm table height. The success rate of the second and third strategies shows an average 63.3% and 73.3%, respectively, for grasping random objects. We also demonstrated these strategies using two intuitive interfaces, a visual interface in rviz and a voice user interface with speech recognition, which are suitable for elderly people. In addition, the robot can select strategies automatically in random scenarios, which make the robot intelligent and able to make decisions independently in the environment. We obtained interesting results showing that the robot adapts to the environmental variation automatically. After these experimental demonstrations, our robot shows the capabilities for employment in domestic environments to perform actual tasks.