RolH:
We tow a 2013 MINI Cooper S, manual tranny equipped, four down. I had a Blue Ox base plate installed on the MINI and it works great, so far. We have towed a Miata and a Jeep Wrangler previously--both four down. We also towed a PT Cruiser, automatic, on a KarKaddy SS for four years with no issues.
Our MINI Cooper S does not have the JCW aero packages, but I don't think that would be an issue for you. One issue you may have with a JCW aero packaged MINI would be loading it on the KarKaddy dolly as the dolly's ramp angle is fairly steep. The MINI's front over hang is quite short so it may not be a problem, but worth checking out before purchase.
The KarKaddy SS is a well engineered, well built product. You cannot go wrong with it. I just sold mine earlier this year as it was no longer needed.
Either way, four down or on a dolly, a MINI Cooper is a great, kick-ass toad. Enjoy and be safe.