I'd guess it's possible. Might even be done in large scale operations. For small folk, I doubt it would be worth the effort: 2 bottles, 2 regs, 2 flowmeters, lots of faffing about getting the mix right, and -- unless you're getting the CO2 free, 2 bottles to rent. And it means you can't easily switch from TIG to MIG.
In which case it's a lot easier -- and you have far more control over the quality -- with 2 bottles, one for TIG, one for MIG.
Yes, I do mix my own, but I would not recommend it. I use a Smith Proportional Mixer. I believe they sell for about $1500.00US. I got one for $50 off ebay. It works well as far as being able to dial in a mix. Switching from MIG to TIG just means changing the mixture dial.
However, it is complicated with lots of connections and two regulators (with restricters removed.) It wastes gas as when you shut it off, there is a lot of gas in all the plumbing, valves etc. Mine also has a slow leak i have not been able to find so if I leave it on overnight, I'll lose 200PSI of argon
I guess it could be done with 2 regulators and flowmeters Y-ed together. If one regulator was set at a slightly higher pressure than the other, it will vent out the other one. Would work if you had two gas solenoids.