Injured Rossi ruled out for 10 more months
"With the objective that Giuseppe Rossi returns to his best physical condition... the most secure procedure consists in two operations," the Spanish side said in a statement on Monday.
The 25-year-old had the first operation in the United States on Friday. He will go under the knife again in four months and will require a further six months to recover.
Rossi, who was born in the U.S, has already missed most of this season after tearing the ligament in the same knee in October. He suffered a relapse in training on April 13.
The initial prognosis was that he would only be out for six months.