The IRS really gives you no incentive to withhold a bunch of your money from your paycheck for personal taxes, if you owe for other tax periods. The case of Weber, 138 TC No. 18, drives that point home loud and clear.
The taxpayer in Weber had a refund coming for overpayment of his personal taxes. He asked that the overpayment be credited to the future. Unfortunately, the IRS had previously assessed the Trust Fund Recovery Penalty ("TFRP" or Civil Penalty 6672) against him as a "responsible person" for payroll taxes in previous tax periods for a failed enterprise.
The IRS snatched the refund and applied it to the TFRP, despite the fact that the IRS was actively collecting the TFRP from other taxpayers deemed "responsible persons" from the failed enterprise. The Tax Court said it was proper for the IRS to do so.
Moral of this story: if you owe taxes from other periods, the IRS is going to take your refund and apply it however they want. If you owe, and have to pay penalties and interest for underpayment, it is better than having the IRS apply your refund at will, while you beg for it back or to be applied differently. So, adjust your withholding accordingly.