Subresultant of two univariate polynomials is a fundamental object in computational algebra and geometry. They are naturally defined by an expression in the roots. Sylvester et al. provided expressions for them in terms of coefficients. They are used in numerous applications. In this paper, we generalize the subresultants of two polynomials to arbitrary number of polynomials, resulting in the so-called multi-polynomial subresultants. Specifically, 1. we propose a definition of multi-polynomial subresultants in terms of roots; 2. we provide an expression for them in terms of coefficients; 3. we show some applications: - parametric multi-polynomial GCD, and - parametric multiplicity.