I was in the same boat as the OP when I first got my 2009 MINI with HiFi. A couple years later I did the swap myself on all the speakers (except tweeters in the A pillar) to the Harmon Kardon ones that came out in 2010. It made significant difference. It's been awhile, but in 2017 I did another swap with the Bavsound Front Sounds Stage (~$250), and that further improved the quality. Everything done was plug and play. Spent a lot, but overall I am satisfied. In hindsight, I would have done the Bavsound and maybe some decent aftermarket woofers for the rear.
The upgrade to Bavsound from the HiFi is a whole other level. If you already have the full HK with HK amp, I'm not sure, but would guess the upgrade would be negligible. Won't hurt to contact BavSound and find out.