This video demonstrates how the pump can be used to deliver both gases. First a couple pumps of blue gas generates a certain pressure. Then we can switch to the red gas for a couple more pumps to generate even more pressure. This illustrates Dalton's Law of Partial pressures since the total pressure will be equal to the sum of the partial pressures. The partial pressures in this case is basically the pressure of blue gas + pressure of red gas.
This simulation can be found on: https://phet.colorado.edu/sims/html/gases-intro/latest/gases-intro_en.html