The effect of alloying the two perovskite-type iron-based superconductors (Ca4Al2O6)(Fe2As2) and (Ca4Al2O6)(Fe2P2) was examined. While the two stoichiometric compounds possess relatively high T-c's of 28 and 17 K, respectively, their solid solutions of the form (Ca4Al2O6)(Fe-2(As1-xPx)(2)) do not show superconductivity over a wide range from x = 0.50 to 0.95. The resultant phase diagram is thus completely different from those of other typical iron-based superconductors such as Ba-Fe-2(As,P)(2) and LaFe(As,P)O, in which superconductivity shows up when P is substituted for As in the non-superconducting "parent" compounds. Notably, the solid solutions in the non-superconducting range exhibit resistivity anomalies at temperatures of 50-100 K. The behavior is reminiscent of the resistivity kink commonly observed in various non-superconducting parent compounds that signals the onset of antiferromagnetic/orthorhombic long-range order. The similarity suggests that the suppression of the superconductivity in the present case also has a magnetic and/or structural origin.