Building Integrated Concentrating Photovoltaic (BICPV) systems make use of optical elements to concentrate the incoming solar radiation on small-sized solar cells with the aim of integrating PV technology into the building. We present a novel conjugate system designed to utilize the merits of both reflective and refractive optics. The optical geometry under study is a dielectric based three-dimensional cross compound parabolic concentrator (3DCCPC) enveloped by a reflective geometry of similar shape whilst maintaining an air gap between them. Monte Carlo ray-trace simulations are used to model and optimize the system configuration. The theoretical analysis shows that the optical performance of the system can be improved by 11% whilst maintaining an air gap of 0.1 mm between the reflective and the refractive surfaces. Experiments are carried out by making a prototype of the proposed system to evaluate the proof of concept. A maximum power ratio of 2.76 was found under standard testing conditions at an incidence angle of 10°. Results show that the average power output from the proposed system increases by 5.46% compared to its predecessor.