Just because the bag says it's one quart, doesn't mean it's one quart. Some are larger, which could hold more.
A Glad Quart Storage bag holds over five cups and still closes, giving you 25% more room.
Shop around, some may be even larger.
And before we start another discussion on why they label them a quart bag when they hold more, that's something you need to take up with them, I don't know why they do that.