Cheesecake Factory Inc. opened the doors Wednesday on its first Puerto Rican outlet, a nearly 10,000-square-foot store in the territory’s capital. The restaurant in San Juan’s Plaza Las Americas shopping center can seat up to 350 guests and marks the first Cheesecake to open since the Calabasas-based chain announced this year it would be opening locations in Latin America, including an eatery in Mexico City. Other restaurants are expected to open in Chile, with expansion into Argentina, Brazil, Colombia and Peru being considered. Cheesecake also is aggressively expanding into the Middle East, where it plans to open 22 stores with franchising management company, M. H. Alshaya. The Kuwait company already operates three locations, including the world’s largest Cheesecake Factory restaurant, a 22,800 square-foot restaurant at the Mall of the Emirates in Dubai. The chain now has 165 Cheesecake locations in the United States and Puerto Rico, in addition to the three in the Middle East. Shares rose 20 cents, or a fraction of 1 percent, to close at $42.06 on the Nasdaq.