Map created by Bret Drager
In the past, there already exists an American Mediterranean Sea.
According to Wikipedia, The American Mediterranean Sea is the combined waterbody of the Caribbean Sea and the Gulf of Mexico. The American Mediterranean has a surface area of 4.319 million km2 and an average depth of 2,216 meters (7,270 ft)
Its basins include those of the southern Caribbean: The Venezuelan, the two Colombians, the Magdalena River and the Gulf of Darién; and the Yucatan Basin. It also contains the Mexican and the Mississippi Basin, both of the Gulf of Mexico.
The American Mediterranean is considered one of the oceanic marginal seas. In addition to numerous small islands, large and small groups of islands, and islets, it includes the large islands of Cuba, bordering the Gulf of Mexico and the Caribbean; of Jamaica, Hispaniola, and of Puerto Rico. All of these islands are among the West Indian islands that separate the American Mediterranean from the Atlantic.
Between the islands, the American Mediterranean Sea contains the following straits: the Florida Straits, the Windward Passage (Paso de los Vientos), the Mona Passage (Canal de la Mona), the Anegada Passage to Guadeloupe Passage, the Dominica Passage to Martinique Passage, St. Lucia, and St. Vincent. Within the Mediterranean, the Straits of Yucatán to the Gulf of Mexico connect with the Caribbean, and by the Panama Canal, built in the 20th century, it is connected to the Pacific.
Composite satellite image of the American Mediterranean Sea. Source: wikipedia