We investigate whether an accelerating universe can be realized as an asymptotic late-time solution of Friedmann–Lem-aître–Robertson–Walker (FLRW) cosmology with multi-field multi-exponential potentials. Such potentials are commonly considered in phenomenological models of dark energy, and at the same time describe the asymptotic regions of the moduli space of string theory. Late-time cosmological solutions exhibit a universal behavior which enables us to bound the rate of time variation of the Hubble parameter. We prove the conditions under which scaling cosmologies are inevitable late-time cosmological attractors of this general class of potentials, independently of initial conditions. As scaling solutions are known analytically, we can characterize late-time observables exactly. Our analysis is general as it does not rely on any approximation nor assumptions on the microscopic origin of the potential. When applied to string-theory, our analytic knowledge of late-time cosmological solutions enables us to single out potentials that can describe an accelerating universe from those which cannot and to quantitatively test several conjectured Swampland criteria.