Simultaneous processing of multiple video sources requires each pixel in a frame from a video source to be processed synchronously with the pixels at the same spatial positions in corresponding frames from the other video sources. However, simultaneous processing is challenging as corresponding frames from different video signals provided by multiple sources have time-varying delay because of the electrical and mechanical restrictions inside the video sources hardware that cause deviation in the corresponding frame rates. Researchers overcome the aforementioned challenges either by utilizing ready-made video processing systems or designing and implementing a custom system tailored to their specific application. These video processing systems lack flexibility in handling different applications requirements such as the required number of video sources and outputs, video standards, or frame rates of the input/output videos. In this paper, we present a design for a flexible simultaneous video processing architecture that is suitable for various applications. The proposed architecture is upgradeable to deal with multiple video standards, scalable to process/produce a variable number of input/output videos, and compatible with most video processors. Moreover, we present in details the analog/digital mixed-signals and power distribution considerations used in designing the proposed architecture. As a case study application of the proposed flexible architecture, we utilized the architecture for a realization of a simultaneous video processing system that performs video fusion from visible and near-infrared video sources in real time. We make available the source files of the hardware design along with the bill of material (BOM) of the case study to be a reference for researchers who intend to design and implement simultaneous multi-video processing systems.