The phrase "a more complete report" is correct and usable in written English.
It can be used when discussing the need for additional information or detail in a report to enhance its thoroughness.
Example: "After reviewing the initial findings, we realized that we need a more complete report to make informed decisions."
Alternatives: "a more detailed report" or "a more comprehensive report".
Here's a more complete report from The New York Times.
A more complete report was due from Afghan and American investigators at the scene within 24 hours.
For a more complete report -- showing individual transactions, expiration dates, mileage and special deals -- there is a charge: $2.95 a month or $29.95 a year.
The New Yorker, September 25 , 1926 P. 13The lure of the Dempsey-Tunney fight drew many people to the Sesquicentennial in Philadelphia and we can now give a more complete report of the exposition.
A fuller account of problems with the sensors on the fuselage, called angle-of-attack sensors, is expected to be part of a more complete report on the crash by Indonesian investigators.
The mine safety officials cautioned that their findings, based on months of testing and hundreds of interviews, were tentative and that a more complete report would be ready in 60 to 90 days.
However, the strength of this review would have been greatly enhanced by a more complete reporting of data in the original papers.
A Commerce Committee aide who insisted on anonymity said that the committee was virtually certain not to hold a hearing this autumn on gas mileage standards, and would wait instead for the more complete report from the National Academy of Sciences.
As this earlier and more complete report from Reuters details, "Iraqi women say registering for government pensions is a bureaucratic nightmare due to corrupt workers who demand money to complete the paperwork.
We would recommend concerted efforts aimed at improving ED SS data quality and completeness, especially more complete reporting of diagnosis codes.
It is also likely that some of the reported increase is due to surveillance artefact, reflecting more sensitive and specific tests for C. difficile toxins A and B and more complete reporting of cases.
