An employer cannot refuse to accept a valid new Form W-4. They can refuse to accept an invalid W-4. If they are claiming that a W-4 that you submitted is invalid, ask them to explain what is invalid about it so that you can fix it.
The employer can take up to 30 days to process a new W-4. They must then adjust your withholding beginning with the first pay period that ends after the 30 days.
You don't claim dependents on a W-4. You claim withholding allowances. An employer, on its own, cannot limit the number of withholding allowances that you claim. However, they might have received a letter from the IRS, called a lock-in letter, specifying a maximum number of withholding allowances that you can claim. If they receive a lock-in letter, they also get a copy of the letter for the employee. They must give you the employee's copy of the lock-in letter within 10 business days after they receive it.
