No, as an individual you are taxed on the income that you are earning from your companies. Companies are currently taxed at a flat rate of 28%, and individuals are taxed on a sliding scale based on their income.

If you only earn R5000. A month from 4 companies that is R20 000 a month, leaves your tax at approximately R 2449.17 a month, which is 12.24%
Your personal tax rate only reaches 28% when you reach an approximate income of R69 000 a month.
Your tax rate is only determined by your age and your taxable income, nothing else. You can be a director of 10 companies, it will have no impact on your tax rate.
Tax planning for small business owners is exceptionally important. By planning your taxes properly, it could help you save tax in the long run.