The sorption of CO2, CH4 and CO2/CH4 mixtures in poly(trimethylsilyl propyne) (PTMSP) and PIM-1 (the first reported polymer of intrinsic microporosity) measured in previous works revealed that, in the multicomponent case, significant exclusion effects cause a decrease in solubility with respect to the pure-gas case, and this effect is more pronounced for the less soluble gas (CH4). In this work we perform a similar experimental analysis on the tetrazole-modified PIM-1 (TZ-PIM), at three mixture compositions (10, 30, 50 mol.% CO2) and three temperatures (25, 35, 50 degrees C), up to 35 bar. The obtained trends for solubility and solubility-selectivity of CO2, CH4, and their mixtures in TZ-PIM are found to be qualitatively and quantitatively comparable to those obtained for other high free volume polymers. Moreover, mixed-gas sorption data collected so far for three materials (TZ-PIM, PIM-1 and PTMSP) are modelled by means of the Non-Equilibrium Lattice Fluid (NELF) model and compared with experimental results. The model was found capable of representing the competitive effects in solubility and solubility-selectivity, in a wide range of temperature and pressure, with a better quantitative accuracy attained at higher temperatures. Finally, by coupling these results with mixed-gas permeation data, an estimate of the mixed-gas diffusivity was obtained, and it was revealed that, in multicomponent conditions, sorption provides a greater contribution to the selectivity than diffusivity, in agreement with experimental findings for similar materials.