We explore the sensitivities at future e−e+ colliders to probe a set of six-dimensional operators which can modify the SM predictions on Higgs physics and electroweak precision measurements. We consider the case in which the operators are turned on simultaneously. Such an analysis yields a “conservative” interpretation on the collider sensitivities, complementary to the “optimistic” scenario where the operators are individually probed. After a detail analysis at CEPC in both “conservative” and “optimistic” scenarios, we also considered the sensitivities for FCC-ee and ILC. As an illustration of the potential of constraining new physics models, we applied sensitivity analysis to two benchmarks: holographic composite Higgs model and littlest Higgs model.