Between the seasons of 1967–68 and 1988–89, Cossotto gave 148 performances at the Met (exclusively leading roles). She was considered an expert in portrayals of major mezzo/contralto roles in mid-19th-century Italian opera such as Leonora (La favorita), Amneris (Aida), Azucena (Il trovatore), Eboli (Don Carlos), Preziosilla (La forza del destino), Maddalena (Maddalena), Ulrica (Un ballo in maschera) and Laura (La Gioconda). She also portrayed Carmen, Mozart's Cherubino, Urbain in Meyerbeer's Les Huguenots, Bellini's Romeo and Marfa in Khovantschina.
In 2005, Cossotto celebrated her 70th birthday with a performance of Suor Angelica at the Théâtre Royal in Liège, Belgium.
Cossotto was married to the Italian bassIvo Vinco for over 40 years (ending in divorce). They had a son.
According to the book Opera, "She [Cossotto] and Giulietta Simionato were the leading Italian mezzo-sopranos of the 1960s and 1970s. She [Cossotto] won plaudits in the annals of operatic history for her wonderful vocal timbre, her perfect singing technique, and the ease with which she could master different registers. Besides singing the great mezzo roles, she also took the outstanding alto parts of the Italian operatic repertoire."
Apart from mezzo and alto roles, Cossotto also sang soprano roles traditionally sung by mezzos such as Santuzza (Cavalleria Rusticana) and Adalgisa (Norma).
Her repertory at the Met included Amneris, Eboli, Adalgisa, Santuzza, Azucena, Dalila, Carmen (only on tour and in outdoor park concerts), Principessa di Bouillon (Adriana Lecouvreur) and Mistress Quickly (which she added in 1985, singing with Giuseppe Taddei as Falstaff).
