"hold correspondence" is correct and usable in written English.
You can use it when you are describing the act of exchanging letters, emails, or other forms of communication between two persons or parties. For example: "The two companies agreed to hold regular correspondence to discuss how to best collaborate on their upcoming project."
This small series holds correspondence between Cornell Woolrich and his friend William Thailing.
The GNM Archive holds correspondence from foreign writers including Frederick Augustus Voigt, also known as FAV, and the author Arthur Ransom.
As well as his missives to three US presidents - Roosevelt, Truman and Eisenhower - the archive holds correspondence with Charles De Gaulle, Gandhi, Nehru and writers, painters and actors including HG Wells, Walter Sickert and Olivier.
As well as corporate records the archive therefore holds correspondence, diaries, notebooks, original cartoons and photographs created by people who have worked for either paper.
The collection holds correspondence of many early faculty members including such prominent 19th century American physicians as John C. Dalton, Jr., John Wakefield Francis, David Hosack, William Macneven, Samuel Latham Mitchill, Valentine Mott, and John Augustine Smith.
Texts by peers including Lenore Tawney, Donald Judd, and Lucy Lippard are presented alongside interviews with a number of Martin's friends and keepers of estates, such as the publisher Ronald Feldman and Kathleen Mangan of the Lenore Tawney archive, which holds correspondence between Martin and Tawney.
I had come to pore over the dozens of authentic Torah scrolls also purchased from Shapira before that fateful summer of 1883, along with a dossier holding correspondence relating to the Shapira affair.
Box 1 holds Correspondence-Study Secretary H. F. Mallory's bound letter book for October 1897 to October 1898, which is the only correspondence preserved from the early years.
Meanwhile, companies have repeatedly told parliament and courts that they do not hold any correspondence or minutes from the Consulting Association, despite their directors attending meetings and paying hundreds of thousands of pounds in fees over a 16-year period.
