A simple model with focus on the electrostatic interaction has been used to examine the complexation of a linear polyelectrolyte possessing variable flexibility with one or several oppositely charged macroions. Composition, structure, and thermodynamic properties of the complexes were obtained by using Monte Carlo simulations. Binding isotherms obtained were Langmuir-type with a quantitative binding up to a neutral complex with a plateau value corresponding to similar to 50% overcharging, the largest overcharging appearing for the stiffest chain. Free energy calculations demonstrated that the complexation of the first macroion becomes less favorable as the chain stiffness is increased, whereas the opposite was found for a complexation of a macroion to a neutral complex. For a neutral complex and with a flexible chain, the repulsion between complexed macroions is strongly screened and the complexed macroions are located near each other. However, for a very stiff chain, the macroions are sequentially positioned along the chain with much fewer polyelectrolyte segments near them and with a considerable effective repulsion between the macroions. Furthermore, our results are discussed using the concept of an overcharged/undercharged complex with respect to both the polyelectrolyte and a macroion as the central species. The location of the small ions was also considered and in particular for a neutral system they are nearly homogeneously distributed in the solutions.