Structural methods have previously been used to perform isolability analysis and finding testable sub-models, so called Minimal Structurally Overdetermined (MSO) sets, Analytical Redundancy Relations (ARR), or Possible Conflicts (PC). The number of MSO sets grows exponentially in the degree of redundancy making the task of computing MSO sets intractable for systems with high degree of redundancy. This paper describes an efficient graph-theoretical algorithm for computing a similar, but smaller, set of testable submodels called Test Equation Supports (TES). A key difference, compared to an MSO based approach, is that the influence of faults is taken into account and the resulting number of testable models as well as the computational complexity of finding them can be reduced significantly without reducing the possible diagnosis performance. It is shown that the TESs in a direct way characterize the complete multiple fault isolability property of a model and thus extends previous structural approaches from the single-fault case.