IMO you're ok.
The hitch weight is based on the tow rating, a JKU is exactly the same with a hitch weight capacity of 350 pounds.
Keep in mind the rear springs may sag more than you want. Also keep in mind the rear axle flanges are a weak spot when you run heavy.

 

Also worth noting, 2016, 2017 and 2018 2 doors have a 350 pound hitch rating when equipped with 3.73 or 4.10 gears.

 

According to my documents the hitch weight limit is 200 lbs on a JK 2 door wrangler. I tow the wrangler behind a Motorhome. I also want to be able to carry a Yamaha S-Max 155 cc with wet weight of 328lbs. Is it possible to change the hitch receiver so that it will carry the extra weight? Would any other modifications need to be made to safely tow the Jeep carrying the scooter?

IMO you're ok.
The hitch weight is based on the tow rating, a JKU is exactly the same with a hitch weight capacity of 350 pounds.
Keep in mind the rear springs may sag more than you want. Also keep in mind the rear axle flanges are a weak spot when you run heavy.

Ok so I’ll have to look again. I thought the Jeep website said 200lbs. I should qualify this post by saying I don’t have a hitch carrier on the Jeep yet but wanted to put one on if I can for the scooter.

 

Hitch capacity depends on towing capacity of the vehicle, tong carrying weight is usually 10% of trailer weigh. So 2000lb trailer will have 200lbs tong weigh,
This is why same hitch can have different ratings.


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Tongue weight depends on towing capacity. Hitch capacity is based on the physical parameters of the hitch.

 

Besides weight, the other consideration is the twisting torque you might put on the receiver when you go over bumps or uneven terrain. When pulling a trailer, that isn't a consideration. I once followed a pickup up a rough trail that had one of those flat platforms for carrying gear in the receiver, and the twisting and rocking broke the platform off the receiver.