Several times recently, I have heard the phrase "on a regular basis" being modified for emphasis, eg "on an extremely regular basis".
Now, I hate the phrase to start with - not only is it unnecessarily verbose*, it doesn't mean what people think it means.
Christmas happens "on an extremely regular basis". Halley's comet passes by the Earth "on an extremely regular basis".
If you mean "very often", why not say "very often"?
I am trying hard not to lose any sleep over this unimportant matter.
*ETA: yes, I know - verbosity implies lack of necessity