  Membrane-induced interactions have been predicted to be important for the
organization of membrane proteins. Measurements of the interactions between two
and three membrane deforming objects have revealed their non-additive nature.
They are thought to lead to complex many-body effects, however, experimental
evidence is lacking to date. We here present an experimental method to measure
many-body effects in membrane-mediated interactions using colloidal spheres
placed between a deflated giant unilamellar vesicles and a planar substrate.
The thus confined colloidal particles cause a large deformation of the membrane
while not being physochemically attached to it and interact through it. Two
particles are found to attract with a maximum force of 0.2~pN. For three
particles, we observe a preference for forming compact equilateral triangles
over a linear arrangement. We use numerical energy minimization to establish
that the attraction stems from a reduction in the membrane-deformation energy
caused by the particles. Confining up to 36 particles, we find a preference for
hexagonally close packed clusters. However, with increasing number of particles
the order of the confined particles decreases, while at the same time,
diffusivity of the particles increases. Our experiments for the first time show
that the non-additive nature of membrane-mediated interactions affects the
interactions and arrangements and ultimately leads to spherical aggregates with
liquid-like order of potential importance for cellular processes.
