I am changing jobs. I've hit the social security cap already. Can I offset the amount taken out for income witholding on my W4 to offset or might that trigger a penalty?

It depends. If you have two different employers which is why you paid an excess in social security tax, then you will see the credit on Schedule 3, line 11 and on the Form 1040, line 31 as a payment towards your taxes.  If you see these numbers you can be confident you can file your return.  The maximum social security wage is $147,000 and tax is $9,114, respectively.

 

A new employer is not allowed to offset any social security tax based on wages paid through a different employer.  This is strictly handled by the IRS in that circumstance.

Thanks. My main question is whether it would be okay if I could adjust the deductions on my w4 to offset the extra social security payments myself, or if that would be prohibited somehow or result in penalties somehow. 

The short answer is yes you can make the adjustment.  The difficulty would be to calculate the adjusted withholding so that you would not get a penalty.

The sake harbor guidelines are:

 

The underpayment penalty may apply if any of these apply:

 

• The amount of tax you paid during the tax year is less than 90% of the tax that you owed for the current year. 
• The amount you paid during the tax year did not equal 100%, (110% for higher incomes) of your taxes owed the prior year. 
• The IRS also says you can probably avoid the penalty if the amount you owe is less than $1,000, after subtracting withholding and refundable credits.

"Typically, underpayment penalties are 5% of the underpaid amount, and they're capped at 25%. Underpaid taxes also accrue interest at a rate that the IRS sets annually."

 

To avoid this situation it is recommended that you adjust your W-4 with your employer or pay estimated taxes.

 

Tax Underpayment Penalty: What It Is, Examples

Underpayment of Estimated Tax by Individuals Penalty