The formation of multiple stellar systems is a natural by-product of the star-formation process, and its impact on the properties of protoplanetary discs and on the formation of planets is not yet fully understood. To date, no detailed uniform study of the gas emission from a sample of protoplanetary discs around multiple stellar systems has been performed. Here we analyse new ALMA observations of the molecular CO gas emission at a ~21 au resolution, specifically targeting discs in eight multiple stellar systems in the Taurus star-forming regions. ¹²CO gas emission is detected around all primaries and in seven companions. With these data, we estimate the inclination and the position angle (PA) for all primary discs and for five secondary or tertiary discs, and measure the gas disc radii of these objects with a cumulative flux technique on the spatially resolved zeroth moment images. When considering the radius, including 95% of the flux as a metric, the estimated size of the gas disc in multiple stellar systems is found to be on average ~4.2 times larger than the size of the dust disc. This ratio is higher than what was recently found in a population of more isolated and single systems. On the contrary, when considering the radius including 68% of the flux, no difference between multiple and single discs is found in the distribution of ratios. This discrepancy is due to the sharp truncation of the outer dusty disc observed in multiple stellar systems. The measured sizes of gas discs are consistent with tidal truncation models in multiple stellar systems assuming eccentricities of ~0.15-0.5, as expected in typical binary systems.