As usual B&S are not completely specific, but they do say that operating the engine at a tilt angle exceeding 15 degrees to the horizontal may cause it to blow smoke:
http://www.briggsandstratton.com/engines/support/frequently-asked-questions/answer.aspx?p_faqid=1378Personally I would say that they seem to be suggesting that exceeding 15 degrees is not acceptable practice. That is a 27 percent slope: about as steep as it is possible to restart a car with manual transmission on, and about as steep as a good handbrake will hold on, with a really huge amount of force on the handle.
If you need to mow beyond 15 degrees, I suggest you use a 2 stroke. The carburetor probably won't work properly of course, but that shouldn't actually break anything.