Mapa got his first professional break when he was cast to understudy, and then replace B.D. Wong in the Broadway production of M. Butterfly. Mapa later played the role on the national tour. Mapa would return to Broadway in an adaptation of L'Hôtel du libre échange by Georges Feydeau and Maurice Desvallières, re-titled, "A Little Hotel on the Side" in 1992. The next year, Mapa was back on Broadway in a Stratford Festival inspired production of Timon of Athens. Off-Broadway, Mapa earned a nomination at the 2001 Lucille Lortel Awards for his performance in the Jessica Hagedorn play Dogeaters, and was featured in every play in the "Whitelands" trilogy, a series of plays about gay Asian men written by Chay Yew; "Porcelain" (1992), "A Language of Their Own" (1995), and "Wonderland" (1999).