  Within mean-field theory we calculate universal scaling functions associated
with critical Casimir forces for a system consisting of three parallel
cylindrical colloids immersed in a near-critical binary liquid mixture. For
several geometrical arrangements and boundary conditions at the surfaces of the
colloids we study the force between two colloidal particles along their
center-to-center axis, analyzing the influence of the presence of a third
particle on that force. Upon changing temperature or the relative positions of
the particles we observe interesting features such as a change of sign of this
force caused by the presence of the third particle. We determine the three-body
component of the forces acting on one of the colloids by subtracting the
pairwise forces from the total force. The three-body contribution to the total
critical Casimir force turns out to be more pronounced for small
surface-to-surface distances between the colloids as well as for temperatures
close to criticality. Moreover we compare our results with similar ones for
other physical systems such as three atoms interacting via van der Waals
forces.
