You can get hitches for most any car on the road today. I used to install hitches for a living, no not a good living. IF and I do mean IF you decide to tow with a supra, and it's an auto, get a transmission cooler, you'll thank me later. Also don't tow anything heavier than 2/3 the vehicle weight, past that and you'll have issues at speed, especially if you haven't balanced the load properly- 60 in front of the trailer axle, 40 in rear.
I also trust draw-tite more than any other hitch manufacturer. From what I've read they do the most testing. It looks like the supra one is rated for 1500 lbs max which is about right. Also the only part of the hitch you'll see is where you put the slide bar in, which is removable and you won't wrack your shins on it. You'll have to trim some of the lower part of the bumper to fit it.