The present investigation describes the final piece of a three-part numerical parametric study on the validation and calibration of the General Method (GM) for the fire design of web-tapered steel members. The GM covers the safety verification of non-prismatic members, as the variable geometry precludes the use of the standard verification clauses. However, no specific guidelines are provided in the fire part of the Eurocode 3 (EN 1993-1-2) regarding its implementation at elevated temperatures, apart from adopting the reduction factors for steel material properties. Following the design philosophy of the Eurocode 3, proposals for the stability check of web-tapered columns and beams have recently been proposed by the authors, leading to safe and more accurate predictions by the General Method for these members in fire. Supported by an extensive numerical framework of over 20000 members at elevated temperatures, as well as the abovementioned calibrations, a novel interaction factor for tapered beam-columns is proposed in the scope of this work, thereby accomplishing the ultimate goal of achieving a unified calibration of the General Method for non-uniform columns, beams, and beam-columns at elevated temperatures.