Hi tivity606!
Thank you for the question. In your situation, it may be better to pay estimated tax payments than try to pay in extra tax through withholding. It all depends on whether you have a profit from the job that sends you a 1099. If your recent 2022 tax return will be similar to what you expect the tax year 2023 will be, then you have an idea of the total tax you owed in 2022 and how much additional you may need to pay in.
To estimate your 2023 tax, use Intuits TaxCaster.
To adjust your 2023 withholding, use Intuits W-4 Calculator.
To understand Estimated Taxes, read this article.
I hope this helps. If you need additional information please post in the comments.