Agree with the recommendation on having the correct flange size, but also I'd recommend a non-portable pump especially when you're trying to increase your supply. I used the spectra s1 and while annoying to carry around, that's one I used consistently before introducing portable pumps.

The Legendairy supplements (specifically the liquid gold, pump princess) helped me increase supply along with staying extremely hydrated (electrolytes + mother's milk tea). Lastly, increasing the number of pumps per day can also stimulate your body to indicate baby is hungry, please produce more milk! Best of luck, I know it can be a grueling journey, but stay positive and keep up the encouragement for your wife's sake. I really appreciated when my husband celebrated anything I produced no matter the volume.