The analytical solution of the Chandler-Silbey-Ladanyi Percus-Yevick (CSL-PY) approximation for multicomponent molecular site-site fluids is presented. The molecules are modeled by a collection of an arbitrary number of hard-sphere sites of any size and geometrical arrangement, provided only that all sites are in contact and the bonding distance is equal to the contact distance between the sites of the molecule. Assuming an additional approximation for the intramolecular correlation between the molecular sites not bonded directly the solution is extended to the case of flexible molecules. A closed-form analytical expression for the compressibility equation of state is derived. In the case of the linear flexible chain model polymer system, this equation of state coincides with the equation of state derived earlier [Y. C. Chiew, Mel. Phys. 70, 129 (1990)]. Comparison of the theory with computer simulation results shows that predictions of the CSL-PY theory for the compressibility pressure of the star polymer system is fairly accurate, while the structural predictions for linear chain n-mers are quantitatively accurate only for the systems of dimers.