We suggest an approach for transport through finite systems based on the Liouville equation. By working in a basis of many-particle states for the finite system, Coulomb interactions are taken fully into account and correlated transitions by up to two different contact states are included. This latter extends standard rate equation models by including level-broadening effects. The main result of the paper is a general expression for the elements of the density matrix of the finite size system, which can be applied whenever the eigenstates and the couplings to the leads are known. The approach works for arbitrary bias and for temperatures above the Kondo temperature.We apply the approach to standard models and good agreement with other methods in their respective regime of validity is found.