Most guys who think they are overrtraining aren't. You have to be continuously building fatigue and micro trauma over the course of months that you can't recover from. This kind of fatigue can take a long ass time to recover from and your performance will go to shit. We are talking a few months, this won't happen because you tripled your volume and workload for a couple weaks, and if you were truly overrtraining it would take you more then a couple days to recover. Months and years...think of overrtraining as a disease if it helps.
What guys often think is overrtraining is just overreaching, and the reality is, as body builders, this useful. We continually build fatigue and microtrauma, often to the point where it hasn't receded fully before we work out again. Yet you still get bigger and stronger.
A simple solution to keep you from overrtraining is to take a deload or some time off with reduced volume to let recovery catch up. You would have to be neglecting this for months and years to be overrtrained.
Even guys who insist they are all about recovery and not over training and take a week off before hitting a muscle again are overreaching a lot of the time, they think they aren't because there performance doesn't take a noticeable hit, but if you are doing a bro split or one muscle group a week vs a higher frequency routine, the effect on recovery is pretty much the same as long as weekly volume is the same.
My advice for your two a day routine is:
Run 2 a days for a while, but make it a planned overreach. So something like, you do 2x a days for 3 weeks, make sure the total weekly volume is much higher than what you normally do, keep the workouts intense. I would do this until I notice a slight decrease in performance, maybe after a week or two, then go for a little bit longer. Once you have blasted for a couple weeks, take 3-5 days off (or with significantly reduced volume).
This is basically dual factory recovery, the advantage to running 2x a days in this situation is you can do more work per week. Take advantage of that. If it was a successful overreach, you should come back stronger then before (so set out some strength goals before going into it).
If you are doing 2x a days just for the sake of splitting up your work even more, I wouldn't bother. If you want to hit things more frequently and increase weekly workload, then I would treat it like a planned overreach and make sure everything gets hit more frequently (leading to more weekly volume). Give yourself the time off after the blast to recover.