In this work it is presented a new design of a TIR lens-mushrooms lens device developed with the Simultaneous Multiple Surfaces (SMS) method. In SMS nomenclature, it is named TIR-R. In contrast to previous TIR-mushroom designs, application of the SMS method to this configuration consists in the simultaneous design of both TIR (total internal reflection) and R (refraction) optical surfaces using extended ray-bundles and the edge-ray theorem. In this paper is presented a basic approach to do the design. In this basic approach, first it is considered the TIR lens as a microstructured surface with infinitesimal flat facets. Afterwards, it is generated a TIR lens with finite size facets from the already designed one. In an advanced approach could be considered the TIR lens with finite facet size and designed simultaneously each facet with a portion of the outer surface of the mushroom lens. With respect to others SMS high-gain devices (as the RXI), the TIR-R concentrator has the following advantages: is a mirror-less device, there is not shadowing elements, and the receiver/emitter element's placement is more favorable for encapsulation and electrical connection. As it is common in the SMS devices, the TIR-R concentrator achieves wide acceptance angle and high efficiency with a low aspect ratio (thickness to entry aperture diameter ratio). For example, a 1256X concentration device has a theoretical efficiency of 100 percent (without optical losses) with an acceptance angle of +/- 1.7 decgrees, and an aspect ratio of 0.34.