In view of the interest that (Fe,Co)₂(P,Si) compounds have as potential permanent magnets, their structural and magnetic phase diagrams are explored focusing on establishing the range where the hexagonal Fe₂P-type structure is observed. In Fe_1.93-xCo_xP_1-ySi_y, the highest Si content prior entering a mixed phase domain is y ≈ 0.5. At high Si content but low Co for Fe substitutions, a structural distortion leading to a body-centered orthorhombic structure occurs. At high Co contents, when the Fe₂P unit cell reaches a critical volume of about 102.4 ų, the samples crystallize in a Co₂P-type orthorhombic structure. Within the Fe₂P-type structural range, the evolution of the unit-cell volume appears to follow the Vegard's law, but this hides strongly anisotropic changes. Simultaneous Co for Fe and Si for P substitutions increase the range where the hexagonal structure is observed in comparison to ternary Fe₂(P,Si) and (Fe,Co)₂P. The samples are ferromagnetic, but with Curie temperatures showing an unusual evolution, uncorrelated to the c/a ratio of the lattice parameters. At low Si content, T_C increases with Co for Fe substitutions. For y = 0.2, the evolution is not significant, while at high Si content T_C systematically decreases with the increase in Co. Large Si and Co substitutions lead to a swift weakening of the magnetocrystalline anisotropy until the easy axis anisotropy turns from the c axis toward the a-b plane. This study guides future investigations by restricting the range where desirable properties for permanent magnetic applications can be expected to 0.1 ≲ x ≲ 0.3 and 0.1 ≲ y ≲ 0.3.