Reading through the NASA Graphics Standards Manual, pages 7.9–11 inform how the iconic worm logo and other graphical elements are to be used on flight-ready vehicles, whether aircraft, spacecraft, or mission payloads. However, it does not mention how to use competing but equally-important elements such as the logos of other space agencies or nations.
For examples of such joint projects, consider the Orion ESM, developed by the ESA, (although it predates the graphics-standards manual), the definitely-never-going-to-happen joint moon mission JFK proposed briefly, or the fictional joint Iris probe in the Martian.
The manual makes it clear that the NASA logo is be the dominant design element unless the US flag is present. How would the authors of the manual recommend dealing with competing design ethics and elements on joint missions (not to mention the bizarre aspect ratio of the US flag compared to nearly any other flag)?