Spatial audio object coding (SAOC) is an effective method to transmit multiple audio objects. Audio systems can provide personalized services under this framework. However, this method causes frequency aliasing distortion, which severely impacts the listening experience. The multi-step SAOC (MS-SAOC) scheme was proposed to enhance the sound quality of each audio object by using residual information. Compared with SAOC, the bit-rate increases three times due to the residual data of multiple objects. In this paper, an efficient multistep residual coding method is proposed to reduce the residual bit-rate of MS-SAOC. A two-level filter is designed to remove redundant residual information, and the limited residual information can efficiently compensate for frequency aliasing distortion. From experiment results, the residual bit-rate is half of MS-SAOC, and the sound quality is maintained at the Good-Excellent level.