Though on paper they say that you can extend your South African tourist visa, it's actually very difficult and almost impossible to get an extension of your tourist visa when in South Africa since immigration handed over the task of tourist visa extension to VFS, a global visa company.
Normally for other visa extensions in South Africa, you have to submit your visa extension application 60 days before your visa expires, but when dealing with tourist visa extensions through VFS the whole process can take up to 90 days or more and probably by then your visa would have already expired and you'll have to leave. In addition, it's costly and wastes time.
Best alternative
Visa run to your home country or a non-neighboring country.
Going back to your home country and re-entering South Africa is the only way you're 100% sure that you'll get a new tourist visa. Alternatively, you can visit a non-neighboring country probably in Eastern or Central Africa then re-enter South Africa.
Tip: Avoid visa- runs to Southern Africa countries that border South Africa such as Swaziland, Lesotho, Mozambique, Namibia, Botswana, and Zimbabwe, this lowers your chances of getting a new South Africa tourist visa unless you get lucky at the border.