Your withholding and your W-4 have nothing to do with how much nonrefundable credits you can get. Nonrefundable credits are applied to your total "tax liability" for the year, before the withholding or other payments are applied, not to the amount that you owe when you file your tax return. Changing your W-4 will not help you get more nonrefundable credits.
On your 2022 Form 1040 the total tax liability before nonrefundable credits is on line 18. The total nonrefundable credits, including the solar credit, are on Form 1040 line 21. On line 22 the total nonrefundable credits on line 21 are subtracted from the total tax liability on line 18, but the result cannot be less than zero. If the total nonrefundable credits on line 21 are more than the total tax liability on line 18, then you are not able to use all the nonrefundable credits, and line 22 will be zero. If Form 1040 line 22 is not zero, you are using the full amount of all your nonrefundable credits.
Withholding is subtracted later, on Form 1040 line 25a. It does not affect the amount of nonrefundable credits that you can use on line 22.
The line numbers on Form 1040 for 2023 are expected to be the same as 2022, but the IRS has not yet issued the final Form 1040 for 2023.
The only way to increase your tax liability so that you can use more nonrefundable credits is to increase your income, so that your tax will be higher. Some ways that you could increase your income, besides getting a raise or a higher-paying job, are to
sell investments with a gain, take an IRA distribution, convert part or all of a traditional IRA to a Roth IRA, or contribute to a Roth IRA instead of making deductible contributions to a traditional IRA.
"Should I claim exempt from tax withholdings . . .?"
Note that you cannot claim exempt on your W-4 unless you meet BOTH of the following conditions.
(1) You had no federal income tax liability in 2022
(2) you expect to have no federal income tax liability in 2023.
For this purpose, federal income tax liability is defined as the total tax on line 24 of your 2022 Form 1040. It is not the amount that you owe on your tax return.
But as stated above, claiming exempt on your W-4 would not do any good anyway with regard to how much you can get for the solar credit or any other nonrefundable credit.
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