My partner does not seem to get enough taxes taken out, whereas I do. I assume it's because they noted more dependents on their W4. I want to see the best approach to avoid owing taxes each year.
Normally, what gets the withholding closer to the tax liability is for the parent with the highest income to claim the dependents in step 3 on the W4. The other parent should skip steps 3 and 4 on the form W4.
Having said that the most accurate way to complete the new W4 is using the IRS estimator tool. The same rules should apply. Only the parent with the higher income should enter dependent information.
Read the W-4 instructions carefully and thoroughly. It tells you what to do. (All 4 pages, not just the front page you turn into your employer.) You go through the instructions one time for both of you, and it will recommend how many allowances to claim on each W-4, and then you each file a new W-4 based on the result of the worksheets. Under the new method, you need to coordinate your w-4s when both spouses work or one person has more than one job.