All are aged in their 50s and from the York area.
One was arrested on March 23 and the three others on April 22.
Police have reissued warnings against identifying the men to make sure the investigation is not compromised.
Call 101, select option 1, and pass details to the Force Control Room. Please quote “Claudia Lawrence” when passing on details.
Alternatively, call Crimestoppers anonymously on 0800 555 111.
For further information visit www.northyorkshire.police.uk/claudialawrence