https://www.mauser.com/fileadmin/user_upload/MAU_Calibers_M03_DE_2015_2016.pdf

.458 Lott is the largest chambering available currently.

Yes a .500 Jeffery would be an excellent addition. The barrel might be thicker again, and perhaps require an even wider barrel channel than the .404 and presumably .458 barrels.

.416 Remington Magnum is another choice.