Designing a pure phase multifunctional diffractive optical element (M-DOE) is a challenging task, as the regular summation of multiple pure phase functions results in a complex function. One of the widely used multiplexing methods to design a pure phase M-DOE is the random multiplexing method. In this method, different pure phase functions are multiplied to mutually exclusive binary random functions before summation. However, M-DOEs designed using the random multiplexing method are prone to scattering noise. In this study, a novel approach based on a modified Gerchberg-Saxton algorithm (GSA) has been proposed and demonstrated for the design of pure-phase multifunctional DOEs. In this approach, the complex M-DOE obtained by regular summation is used as a reference, and with suitable constraints, the amplitude component of the complex M-DOE is transported into the phase component, resulting in a pure phase MDOE. This modified algorithm is called Transport of Amplitude into Phase based on GSA (TAP-GSA). This method has been demonstrated on a well-established incoherent digital holography technique called Fresnel incoherent correlation holography (FINCH). In FINCH, it is necessary to multiplex two-phase masks, which can be achieved using random multiplexing or polarization multiplexing, resulting in reconstruction noise and low light throughput, respectively. Under low-light conditions, random multiplexing is a better choice than the polarization multiplexing method. The M-DOE designed using TAP-GSA for FINCH improved the light throughput and exhibited a higher SNR in comparison to the random multiplexing method.