"another layer of complication" is a correct and commonly used phrase in written English.
It can be used when you want to describe a situation or problem that adds more difficulty or complexity to an existing situation. Example: "The company's financial troubles added another layer of complication to the already difficult project."
Buying local media adds another layer of complication.
A general election due on November 28th adds another layer of complication.
Mr. Cuse and Mr. Lindelof were immediately taken to task on Twitter and fan blogs for adding yet another layer of complication to the show.
Occasionally Mr. Everson adds yet another layer of complication to his work by fabricating events that he appears to be documenting.
At the age of nine, I was whisked off to Africa, to Northern Rhodesia, with my mother, where another layer of complication emerged: I found myself attracted to the young black servants.
Mr. Lamburini, who was taken to Bellevue Hospital Center, has not been cooperating with the police, officials said, adding another layer of complication to the case that has already sent investigators in several directions.
So custodians are understandably wary of another layer of complications.
But also because of stereotypes, North American tipping culture has another layer of complications.
I had no clue how to behave or what to expect from another mate, not to mention the men I was connecting with had no experience with a woman with children, posing another layer of complications.
In fact, the models tended to add a layer of complication to what he fundamentally believed was the relationship between photographer and sitter.
Meanwhile, there is the added layer of complication provided by the fact that the British Olympic Association is also keen to make the most of the unprecedented revenue raising opportunity that the Games provide.
