Many modern radio telescopes employ an observational strategy that involves maximizing the use of their available spaces (cabins), outfitting them with various receivers at different frequencies to detect incoming signals from the sky simultaneously or individually. The Large Latin American Millimeter Array is a joint venture between Argentina and Brazil consisting of the installation and operation of a 12-m aperture Cassegrain telescope. It features three available cabins for instrumentation and plans to install six single-pixel heterodyne receivers, covering different bandwidths in the 30 to 950 GHz window of the electromagnetic spectrum, in its two lateral Nasmyth cabins at different phases of the project. Therefore, it is crucial not only to design a tertiary optical system that couples the antenna beam to those receivers but also to do it in a scalable way. The primary goal for the design is to simultaneously maximize the antenna efficiency while minimizing optical aberrations for all receivers, both fundamental aspects for the optimal functioning of cutting-edge astronomical instruments. We present the entire design process, starting from the quasi-optical approach based on the propagation of a fundamental Gaussian beam mode, continuing with the validation of the design based on physical optics simulations, and ending with a tolerance analysis of the system. As a result of this process, a frequency-independent tertiary optical system has been achieved for almost all the receivers, which is expected to provide high optical performance for the radio telescope.