Once you pay the employee enough wages to hit the max tax wages/amounts for the year the taxes will automatically stop.
Note that prior pay from another employer doesn't count: Each time an employee starts a new job, the taxes start over.
If this results in the employee paying to much for an employee-paid tax, like the employee portion of SS and Medicare, the employee will get a refund on their taxes for the overpaid amount.
Company paid taxes, however, don't work that way. Where an employee works multiple jobs in a year, each employer pays up to the max tax.
