If you have an employee who is exempt from state unemployment insurance (SUI) tax, follow the steps for setting up an employee who is exempt from specific taxes. If you are not sure if an employee should be exempt from SUI tax, consult your tax advisor (additionally, we have a non-exhaustive list of "who is exempt" here).
You must withhold and pay Social Security taxes for a new employee who has already reached the yearly wage cap at another company. The employee recovers any overpayments when he or she files personal yearly tax returns.
In some states, directors and officers of corporations are exempt from State Unemployment Insurance (SUI). However, those who don't pay SUI usually have to pay Federal Unemployment Tax (FUTA) at a higher rate. Consult your tax advisor for more information.