I haven' t hunted with the .376 Steyr yet. But here are a few of the sites with information I have found concerning it:
http://www.african-hunter.com/the__376_steyr.htm
www.chuckhawks.com from this site go to Rifle Cartridges and look
for .376 Steyr
also there is information to be found at Google.com under " .376 Steyr"
Hornady factory loads for this cartridge, so cases and ammo are available. There is also a very good selection of .375 bullets for the reloader. The .376 Steyr provides near .375 H&H performance from a standard length action. And should be a very good " Dangerous Game" gun in a Mauser action. Of course it would be no problem at all to develop reduced loads for any medium sized game in the Americas. (And with a well shaped bullet " ie. 250 grain Sierra or a 260 Nosler should be fairly flat shooting for all medium game. Speer also makes a 235 grain semi-spitzer that could be used to work a good " deer" load.)
Lots of possibilities!