Some browsers have implemented a version of the not-yet-standard, Resource Timing API where you can collect some of this information.
Some browsers may have some of this info available to browser extensions as part of their developer tools support, but that would require the installation of a custom extension, not something that could be done from a regular web page.
For very specific operations where you control the calling code or you know the calling code, it is possible to instrument some things. For example, if you know that all ajax calls go through one particular function, you can hook that function and it's completion handlers and monitor all ajax calls.
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…