As demand grows for efficient, localized processing in edge and in-sensor computing, novel architectural approaches are essential to meet low-power, high-density requirements. Memristor Cellular Nonlinear Networks (M-CNNs) offer a promising path forward, leveraging the unique properties of memristors for adaptable and scalable computation. This paper presents a study of novel M-CNN cell configurations designed to enhance computational versatility and address operational challenges in M-CNN-based systems. By leveraging memristor technology within CNN cells, we propose three distinct configurations: (1) incorporating parallel and series resistive elements for refined control over cell dynamics, (2) introducing a fixed bias voltage to expand computational capabilities, and (3) integrating the Full-Range CNN (FR-CNN) model into M-CNNs for the first time. The proposed topologies are evaluated through dynamic route maps (DRM) and vector field analysis to systematically assess stability and performance across varying design parameters.