On the full size QC you have access to 8 presets per bank, and you do have Preset Up and Preset Down footswitches, so that would fix your problem.
BUT, and it’s a BIG BUT, you then encounter another problem, one which I think is THE ABSOLUTE worst feature of the QC and which I, and others, have been banging on at Neural to change for the last 3 years since I bought mine - and of course in typical Neural fashion, they have ignored this very valid request. The problem I’m talking about is that in order to change Mode on the full size QC you have to press the Tuner and Preset Down button at exactly the same time - which introduces the significant risk that if you accidentally press the Preset Down f/s a fraction of a second before the Tuner f/s then you accidentally change Preset right in the middle of your amazing solo. It is the dumbest thing about the QC, it could have really awful consequences, and there is a simple solution, which is to add a menu option to make Preset changing a long press only. But as I say, Neural haven’t listened. The possibility of doing this when playing live makes me so nervous that I’m actually considering switching to the QC Mini if it uses a different f/s combination to change Mode, but from what I see it doesn’t….
In fact, one person on this forum was so bothered by this he has posted a 3D printer file for a footswitch blocker, which goes around the Preset Down f/s, so you simply can’t accidentally press it. It’s like a plastic doughnut, it has a hole in the middle so you can operate the f/s with your finger but not your foot, and it works brilliantly.
Your best solution then would be to use Midi; I now have my full size QC set up with a WIDI dongle, which is paired with my iPad running StageTrax 3.
Now whenever I select a new backing track, every function I need happens automatically on the QC via wireless Bluetooth; for example just by selecting the backing track I want, the WIDI commands will select the correct QC Preset, Open Gig View, Open Looper U/I at the specific point in the song, start Looper Record, Start Looper Overdub etc etc. It’s a foolproof and safe way to do things, and it’s now the ONLY way I use the QC live these days, all of which has led me to the conclusion that the QC is a great studio tool, but not actually that great for live use, and it seems the Mini is even less so.
Of course this may not help you if you don’t use an iPad/Backing tracks etc, but another option if you only have a small MIDI footswitch is to assign the MIDI switches to change Mode, so you don’t have to double press on the QC itself to do this, then keep the QC in Preset Mode for changing Presets on the QC itself. You then don’t need a Preset +/- Midi command.
And the last option of course if you do use backing tracks and don’t want to faff about with Bluetooth dongles etc is to get a Helix Stadium, and use Showcase to fully automate everything!