Surface-related multiple elimination (SRME) is a solid and effective approach for primary estimation. However, due to the imperfections in data and method multiple energy leakage is commonly seen in the results of SRME-predicted primaries. Assuming that the primaries and multiples do not correlate locally in the time-space domain, we are able to extract the leaked multiples from the initially estimated primaries using multi-domain local primary-and-multiple orthogonalization. The proposed framework consists of two steps: an initial primary/multiple estimation step and a multiple-leakage extraction step. The initial step corresponds to SRME, which produces the initial estimated primary and multiple models. The second step is based on multi-domain local primary-and-multiple orthogonalization to retrieve the leaked multiples. Multi-domain indicates that we first extract the leaked multiples in shot domain, and then the residual can be further extracted in common-offset domain. Thus, we can obtain a better primary output which has much less leaked multiple energy. We demonstrate a good performance of our proposed framework on both synthetic and field data, where it repairs the leakage of standard global adaptive subtraction.