"each design" is correct and can be used in written English.
You can use it to refer to the individual components of a collective group, e.g. "Each design in the collection has its own unique features."
We've hired two professional jewelry designers who each design an exclusive line -- about six styles each -- for Women's Bean Project.
Remember, each design is an original, and represents the hard work of your designer.
Each design reflects a cultural odyssey through fashion.
Because of space, she only carries one of each design.
Each design, it seems, has its own merits.
Each design is different, and each design literally leads him to the next, much like the melding of melody and lyrics.
We were told to divine the passion of each design with respect to its era.
That might help explain why each design puts too much emphasis on the towers themselves.
"May each design inspire hope and trust," says a message tucked in with the angels.
Conversation was constant as Mr. Holtzman weighed each design decision out loud.
Each design improves the quality of life for people with dementia in different ways.
