Successfully apologizing for an apology would seem to demand a deft rhetorical touch. The implied message would be: I did not mean my earlier apology, but I do mean this apology. 

Josh Compton

https://www.sciencedirect.com/science/article/abs/pii/S0363811115300825?via%3Dihub

Regretted apologies create a unique rhetorical situation, possibly leading to an apology for an apology. This essay draws on the work of Benoit’s (1995) image repair typology to survey attempts to repair image when the offense is an earlier attempt at image repair. Two case studies are offered—one in politics and one in entertainment—to assess image repair efforts after regretted apologies. Implications for image repair analyses are offered, as well as suggestions for further work to add nuance to image repair theory.

Compton, J. (2016). Sorry sorries: Image repair after regretted apologies. Public Relations Review, 42(2), 353-358.http://dx.doi.org/10.1016/j.pubrev.2016.01.002