I would chain it and hope you aren't too hard on the current transaxle. Unless you find yourself realy needing to claw your way out of something you should be fine. If you are concerned yet, then it is time to trade up while the going is still good.

No, you will not be able to "add" a locking differential to your tractor. There just is not enough "marketing pressure" to support the OEMs offering this feature across the entire range of machines. Nearly everything that is built today has some sort of "price point goal" to meet before the machine ever gets to the point of manufacturing it. This essentially cuts out such "amenities" as locking differentials on the low end stuff. To get a locking differential you will need to climb a bit higher on the money scale. BUT......there are many ways you can increase your traction without a locking diff. More aggressive tires (ag type lug treads), tire chains (my favorite), liquid ballast in the tires, wheel mounted weights or frame mounted "suitcase weights" are some of your options. You ABSOLUTELY DO NOT want to weld the differential gears because after that, you will never be able to make even simple turns with the steering.

I forgot to address a detail you mentioned in your OP. You, like a lot of folks, might think that without a lock-up differential......only ONE wheel "pulls". This is not the case at all. So long as each wheel has sufficient grip to prevent "wheel slip" or spin, the power flow is divided equally (50% to each) between the wheels and they will move across the terrain at roughly the same speed. When the grip of ONE of the tires falls below an arbitrary (varies with a number of factors) traction point (causing the tire to "break loose" or spin), 100% of the power will shift to that wheel and the spinning wheel will be rotating at TWICE the speed of when both wheels were turning equally. I have heard people argue till the cows come home over WHICH wheel "pulls" in a "single traction rear end" (which is not even a good, accurate description of the component anyway).

I have to wonder if you understand what the first two letters in the model # of your tractor mean?

YT stands for "yard tractor". YT's are somewhere between the simple, light duty LT or lawn tractor and the more robust GT's or Garden Tractors. I get the impression that you are about to ask your YT to perform the sort of work that a GT is designed to do. For sure, you could install Ag type bar-tread tires on the rear and load those tires with liquid ballast. In addition, you could also install rear-wheel weights to increase traction even further.

Tractors are just like the proverbial chain that might have one weak link in it. With your YT, it's hard to say what might turn out to be the weak link but suppose for a second that you manage to make those back wheels really stick so that every horsepower that engine can generate gets transferred to the wheels that won't spin. Maybe the engine to hydro drive belt slips or breaks. No big deal. It's only a belt.

But if the hydro itself breaks or a gear in the trans-axle lets go, then you might not like the price of repair. Even if there is warranty still on this tractor, the mods you make might give the dealer the necessary "out" to deny your claim. Just something for you to ponder.

Wow thanks everyone for the response!
You really gave me an education and now I know what my options are.

I didn't realize there was a difference in LT, YT, GT, but thats what I get for listening to the local Home Deopt or Lowes guys. Lesson learned!

Ok well I decided not to add traction and let my mower tell me what it can / can't pull. I pulled the aireator and rake without problems on 90% of the yard, and the other 10% will just have to do without! Not ready to spend that kind of money on a GT when I could push an aireator or rake and get a workout instead.

I appreciate all your input it helped me alot!

I had tha same question 2 years ago. How do I improve the grip on my LT? Simple answer is an LT is an LT... Light duty. I found out the hard way when I started to really work my MTD hard. Trying to tow a weighted core aerator or even towing a rake would cause a loss in traction. I would place a 50lb bag of fertiliser on the back of the LT for added weight and left air out of the tires, Anything I could do to keep momentum. All was well until I started having minor problems at first, strange noises or vibrations, belts stretching or failing. Followed by more serious bushing failures or even bending or cracking parts of the LT. I eventually gave in when the maintenance costs began to escalate.
I kept an eye on eBay and eventually bought a 20 year old GT for the heavy work in the yard for relatively small money. A Kubota B7100. 4 wheel drive and diff lock.
All ths stuff that used to make my LT sweat and groan is hardly noticable on the bota... It'll chugg away all day long doing very heavy work.

If it is within your means, I would recommend a similar route.
I still use my LT for mowing. I overhauled it last year. I repaired all the worn bits and its good to go for another few years easily. All the heavy work is now exclusively done by the bota.

Great simple idea quincy! If I do any aerating on my yard, you can bet it will be done with my 58 year old Cub. Leave the Simplicity to do the mowing and working with the Johnny Bucket Jr.

I wonder if I fabricate a lunch box locker wound people pay enough to make profit.