Tim's advice is spot on and needs to be investigated
Kendall carries a couple of variants but they all carry the following disclaimer
Perhaps I haven't hit on the right product but I couldn't find any without the following info.

From Kendall's site
Applications


  • Service fill of conventional differentials in passenger cars and trucks
  • Top-off only of limited-slip differentials in passenger cars and light trucks (1)
  • Service fill of differentials, final drives and transfer cases in some off-highway equipment
  • Non-synchronized manual transmissions in trucks, buses and heavy equipment where the manufacturer specifies an API GL-5 or MT-1 gear oil

(1) Note: For complete drain and refill, many limited-slip differentials may require the manufacturer’s specified gear lubricant or supplemental additive. Refer to the owner’s manual for specific requirements.