Combinatorial testing (CT) has been proven effective in revealing the failures caused by the interaction of factors that affect the behavior of a system. The theory of Minimal Failure-Causing Schema (MFS) has been proposed to isolate the cause of a failure after CT. Most algorithms that aim to identify MFS focus on handling a single fault in the System Under Test (SUT). However, we argue that multiple faults are more common in practice, under which masking effects may be triggered so that some failures cannot be observed. The traditional MFS theory lacks a mechanism to handle such effects; hence, they may incorrectly isolate the MFS. To address this problem, we propose a new MFS model that takes into account multiple faults. We first formally analyze the impact of the multiple faults on existing MFS identifying algorithms, especially in situations where masking effects are triggered by multiple faults. We then develop an approach that can assist traditional algorithms to better handle multiple faults. Empirical studies were conducted using several kinds of open-source software, which showed that multiple faults with masking effects do negatively affect traditional MFS identifying approaches and that our approach can help to alleviate these effects.