Strong interactions produce a rich spectrum of resonances which decay into three or more hadrons. Understanding their phenomenology requires a developed theoretical framework to extract parameters from experimental data and Lattice QCD simulations of hadron scattering. Two classes of relativistic three-body approaches are currently being pursued: the EFT-based and unitarity-based one. First, I will summarize the essential characteristics and results of these formalisms. Next, I will highlight certain aspects of both approaches using an example of a three-particle scattering process involving a bound state in the two-body sub-channel. It can be considered a toy model for nucleon-deuteron scattering and was used to explore formal features of the three-body methods. In particular, I will present numerical solutions for the amplitudes obtained from integral equations of the EFT-based approach. I will show a simple generalization of the unitarity-based framework, which includes all relevant open channels and describe its analytic properties near the physical energy region. Finally, I will explain the physical relevance of those studies and talk about possible future extensions.