We investigate the morphologies of adhering vesicle triplets as a function of volume-to-area ratio encoded by the reduced volume in strong and weak adhesion regimes. In the strong adhesion regime, the morphology change of the vesicle triplet depends on the arrangement of vesicles. By decreasing the reduced volume, a triangular triplet composed of three spherical caps with a trifurcated flat contact zone deformed to a compact spherical shape with a sigmoidal contact zone, whereas a linear vesicle triplet composed of pancake-shaped vesicles sandwiched between two spherical-cap vesicles with a flat contact zone deformed into a compact spherical shape with biconvex interfaces. The morphologies of vesicle triplets with flat contact zones are reproduced by the so-called two-tension model based on the total energy consisting of bending energy, adhesion energy and surface energy, where the surface tension in the noncontact zone is different from that in the contact zone. When the flat interface deforms, the two-tension model is no longer applicable. The compact spherical triplets with curved interfaces can be reproduced by introducing geometrical constraints requiring that the total area of the non-contact zones is minimal, thereby confining the aggregate to a spherical cavity; this is referred to as the cavity model. In the weak adhesion regime, vesicle triplets with either a triangular or linear topology deform into prolate-based triplets by decreasing the reduced volume.