We provide a version of the classical result of Kowalski and Słodkowski that generalizes the famous Gleason-Kahane-Żelazko (GKZ) theorem by characterizing multiplicative linear functionals amongst all complex-valued functions on a Banach algebra. We first characterize maps on A-valued polynomials of several variables that satisfy some conditions, motivated by the result of Kowalski and Słodkowski, as a composition of a multiplicative linear functional on A and a point evaluation on the polynomials, where A is a complex Banach algebra with identity. We then apply it to prove an analog of Kowalski and Słodkowski’s result on topological spaces of vector-valued functions of several variables. These results extend our previous work from 3; however, the techniques used differ from those used in 3. Furthermore, we characterize weighted composition operators between Hardy spaces over the polydisc amongst the continuous functions between them. Additionally, we register a partial but noteworthy success toward a multiplicative GKZ theorem for Hardy spaces. © 2026, University at Albany. All rights reserved.