A filtration system for clarifying a cloudy beverage from at least one tank in which dregs have formed, the clarifying occurring through a cross-flow filtration. The filtration system includes: a first filtration module having a first filtration element, the first filtration element including a first channel having a first diameter; and, a second filtration circuit located in parallel to the first filtration circuit, the second filtration circuit including a second filtration module having a second filtration element, the second filtration element including a second channel having a second diameter, the second diameter being larger than the first diameter. A method for filtering a cloudy beverage from at least one tank in which dregs have formed, the method using the just-described filtration system.