Decoupled hydro-shearing has been a decades-long paradigmatic mechanism of fluid-induced seismicity. A surging alternative is coupled hydro-mechanical triggering, largely based on the theory of linear poroelasticity. Unfortunately, seismicity source fractures and their geometric and physical alterations to a canonical poroelastic system are rarely accounted for, and seismicity is typically forecasted using a Coulomb stress rate model without producing catalogs. Here, I present a new framework for modeling fluid-induced seismicity in arbitrarily fractured nonlinear poroelastic media. The hydro-mechanical triggering is modeled using our Jin & Zoback (2017, https://doi.org/10.1002/2017JB014892) computational model that resolves both fracture fluid storage and nonlinear flow in addition to full poroelastic coupling. Seismological modeling is achieved stochastically by generating stress drops based on the full inter-seismic poroelastic stressing history. The two steps are sequentially coupled and advanced in time via a new prediction-correction algorithm, allowing for fracture stress updating and synthetic event catalog assembly. To demonstrate model capabilities and effects of fractures and full coupling on overpressure, stress and seismicity, I perform three microseismic-scale numerical experiments by progressively adding fractures and poroelastic coupling into a diffusion-only base model. Some previously unknown mechanisms are elucidated. In contrast to existing models, my model produces repeaters and linear clustering of seismicity. Poroelastic coupling enhances the clustering, inhibits near-field seismicity over time while increasingly favoring remote triggering, and overall significantly reduces the event population. Meanwhile, some seismic source statistical characteristics including the Gutenberg-Richter scaling relation overall remain unaffected, and the curious -value elevation for microseismicity can be attributed to a mechanical origin.