The phrase "another plate" is correct and is commonly used in written English.
It can be used in a variety of situations, but it is most often used to refer to an additional dish or serving of food, or to request one. Example: Could you please bring another plate? I want to try a bit of everything on the buffet. In this example, "another plate" is used to request an additional dish to be able to sample all of the items on the buffet.
Exact(60)
Transfer to another plate.
He never had another plate appearance.
The waiter appeared with another plate.
Spread bread crumbs on another plate.
Place another plate on top and flip both over together.
Without a pause, Lenny smacked his side of the table, sending another plate to the floor.
Everyone loves tapas but sometimes you can't face another plate of patatas bravas.
Put the flour on to another plate and the beaten eggs in a mixing bowl.
Mr. Greenwood revealed that there had been another plate, for the lower jaw, in his family.
Too many wine bars have inconsequential selections, as dull as another plate of stale prosciutto.
On another plate you are given a glass of strawberry water and strawberry and rhubarb sorbet.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com