Greetings Joerg, if I waited a few more days it would be the 11th anniversary of your message. I have a book written in 1919 about the Platter Family in America and it indicates that the father & grandfather of the Joseph Platter (b.1725) who came to America in 1765 were born in Erlenbach, Switz. and moved to Saarbrucken, Ger. about 1701.
Going back further, the book says that the Platter name goes back to the area of the village of Grenchen on the Saaser fork of the Visp river in the Canton of Valais (Wallis).
A Thomas Platter in the 16th century wrote that the name went back into the 14th century, attributing it to having a house on a "wide place" (Platte).