Particles interacting via a non-equilibrium fluid often violate the principle of reciprocity after the fluid is coarse-grained away. The lack of reciprocity means that neither energy nor momentum are conserved and can be continuously extracted from the surrounding fluid medium. These systems are inherently `active', capable of generating behaviors seen in active matter, such as self-propulsion, flocking, and pattern formation. Non-reciprocal interactions are often engineered through asymmetric pairwise forces or designed particle interactions. This thesis presents an alternative approach where non-reciprocity emerges naturally from multibody effects in systems of identical particles with reciprocal pairwise interactions. Through experiments and simulations, we explore the consequences of the non-reciprocal multibody interactions on the dynamics, structural assembly, and mechanical properties of acoustically levitated particle rafts. Specifically, we demonstrate how multibody interactions drive spontaneous self-propulsion and limit-cycle dynamics in a minimal three-particle system and avalanche-like excitations in crystalline rafts. Furthermore, the multibody effects enable unique structural configurations, such as self-assembled particle rings, inaccessible with purely pairwise interactions. Finally, we show how multibody interactions alter the mechanical properties of large crystalline rafts, introducing anomalous transverse force components when interactions are modeled as effectively pairwise. Our findings highlight the fundamental role of multibody non-reciprocal interactions in driving emergent collective dynamics and structural transformations in multi-particle systems with fluid-mediated interactions.