The renormalization-group theory of the d=3 tJ model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, and further/first-neighbor interaction strength ratios. In addition to the tau_{tJ} phase seen in earlier studies of the nearest-neighbor d=3 tJ model, the tau_{Hb} phase seen before in the d=3 Hubbard model appears both near and away from half-filling. These distinct tau phases potentially correspond to different (BEC-like and BCS-like) superconducting phases.
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