I'm sorry, Dave. I'm afraid I can't do that.
No worries. I have trouble understanding why someone would want a class-bases system (other than for legacy reasons) unless they were looking for at least a bit of niche protection.While I'm fully in favor of a class based system I am fully against niche protected class systems.
Class-based systems provide two benefits over a gestalt system:
1. It's easier for beginner to grok. "Ima play a fighter. Hit stuff." Or, "Ima play a wizard. Pew pew pew." This is easier than building up custom characters from point-buying abilities, spells, and skills, Buying off the rack has its advantages.
2. It allows for a constellation of abilities that provide for some degree of specialization/niche protection for a class. Whether it's very granular (only thieves can detect traps, only assassins can use poison, only monks can kung fu, only paladins can annoy the heck out of you) or very meta (fighter hit stuff good and get hit, wizards cast big boom), that's what the class system traditionally does, IMO.
5e is good at (1), not so good at (2). Whether that's a feature or a bug ... eh, who knows.