Wife almost flipped current tractor getting too close to ditch at end of driveway. She stopped and got me. Happened years ago. Pulled it back with chain and Jeep. Now I outline the area with snowblower at least. Once berm there no chance of going down into ditch. Tell Old Man Winter we are done for this Season!
Yeah, they can be tippy! Some worse than others. I think your 2032R is much more stable than my 3033R or 750, it felt a lot like my old 855, which was a very stable machine. My only issue with the 855, other than its 33 years of age, was its curb weight being too low for what I was doing with it.
The worst near-flipping incident for me was dragging a 5000 lb. oak log off my trailer with my old Deere 855 MFWD, which was almost identical to your 2032R in wheelbase and weight, but only 23 hp. In any case, because of tight quarters, I had a chain from the log to my loader, dragging sideways when the log rolled off the trailer and lifted the rear of that little tractor off the ground like you flipping a teaspoon off the counter with your finger. I was right next to one of my log piles, so I was headed fast toward being pinched between the tractor and log pile, as my mind raced for which way to push the loader stick to correct the situation.
Obviously things worked out, I'm still here, but it reminded me of how slowly your brain can process a quickly-changing situation like that. You may always tell yourself you'll just push the loader stick forward and dump the load if things go sideways, but making your hand do that when you're in the process of tipping over and disoriented, is easier said than done. You're not as quick as you think you are... or at least I'm not.
Because a primary use of my tractor is moving logs, I ended up going with the 3033R, as much as I preferred the 2038R for every other job I do with the machine. The lift capacity of the 320R loader is superb, and I have an absolute crap-ton of weight to hang on the rear for ballast, in addition to loaded rear tires. But this machine is a lot heavier and taller than the 2-series, without being much wider, which makes me more nervous on hills when using it for other tasks. Every tractor is a compromise!