In multistate non-Hermitian systems, higher-order exceptional points (EP) and exotic phenomena with no analogues in two-level systems arise, which have spawned intriguing prospects. A paradigm is an exceptional nexus (EX), a third-order EP as the cusp singularity of multiple exceptional arcs (EAs), that has a unique, hybrid topological nature. Using Bose-Einstein condensates to simulate the dynamics of a dissipative three-state system, we observe an EX formed by the coalescence of two EAs with different EP geometries. These exceptional structures are realized by controlling only two real parameters even in the absence of symmetry, and originate from the different roles of dissipation in the strong coupling limit and quantum Zeno regime, respectively. Our work paves the way for exploring higher-order EP physics in the many-body setting of ultracold atoms.