There are two types of 404 errors: WordPress-generated, and server-generated.
In some server environments, 404s could be inaccurately displayed by the server in cases of CPU overload or due to certain instances of misconfiguration, etc. Usually server-generated 404 errors will say something like “Nginx” or “Apache” at the bottom of the page (depends on server type).
In other situations, “false positive” 404 errors could be generated by WordPress (PHP) because security plugins are blocking access to loaded resources:
Why am I sometimes getting a 404 error when I try to update a page with Elementor?
https://wordpress.org/support/topic/getting-false-positive-404-errors-with-newest-update/
Try disabling any security plugins, clear caches, and refresh the page. Security modules such as ModSecurity installed on your server could also potentially be the cause.
It could also be caused by a poorly coded theme or plugin. Check if there’s a common theme or plugin installed on all the sites involved. And if this issue only occurs on Media Temple hosting, it’s possible they have something misconfigured, or even that your server is under too much load…