How high, exactly?
Why? What would make South Africa so much more attractive than, say, New Zealand? Would the Afrikaners not feel threatened by the risk of becoming a minority of the white population?
Why on Earth would South Africa do this?
1. the figures from migrationpolicy.org are suggesting roughly 600k per year before the 1924 quota act.
2. It's closer to europe than New Zealand, and what the Afrikaners want won't really matter as long as the Crown still has some control over them. The British would also like this as these immigrants would be much more loyal than the Afrikaners and if the Afrikaners are intelligent enough they'll do everything they can to assimilate the white population. Look at the white population of America, it is most definitely not WASP based but they all speak english and participate in a overtly anglo based culture why couldn't the same outcome happen to south africa? If a intelligent group of Afrikaners realize this they can seriously bolster their position in the country alongside making the threat of black-majority rule less terrifying
3. In a TL I'm writing the Prime Minister that comes to power after a ridiculously controversial National Government will make it so anyone can immigrate to South Africa as long as they have the necessary funds to support themselves for 6 months/have a job lined up. The reason for this is because he's a big libertarian and a believer in that ideological strain and thinks anyone who can afford and is willing to work should be able to migrate to South Africa.
Take the number of there being around 5 million white south africans right now in 2016
Assume that South Africa after 1924 does what it can to be a attractive place for immigrants and gets roughly say 2 million people over several years. This growth calc that says the rate of growth on average from 1930s to 2016 is on average would hypothetically be 1.3% this brand new population in this Alt south africa would have an extra 6 million white people essentially making it so the white population is 11 million instead of 5 million. White South Africans would go from being around 8% to 18%. That's not accounting for the high amount of post WW2 migration which could possible take the white population from 18% to around 30%. Add in the post soviet diaspora and the scenario and whites will form a very large minority in the country and in many regions be the majority.
To answer the OP in the TL I'm writing South Africa would be a mostly stable and economically successful pluralistic society where no one race reaches above 40% of the population, Apartheid would never develop but the greatest problem would end up being Far-Left African Nationalistic Terrorism and Far-Right White Nationalist Terror. A scenario similar to Italy's Years of Lead. Another problem would be income inequality and the fact the far left and far right are capitalizing on increasing stratification between classes.
I've been doing a lot of research for this TL so if anyone wants to hit me up and tell me something I'm saying is just so obviously wrong please pm me cause I don't want to post absolute dogshit to the site.