You can calim as many dependents as you like, but as you said, you need to keep in mind that at the end of the year you may be short on your tax withholding, which means you may owe taxes plus interest on the underpaid amount.
I don't know if you would really need to claim 20 dependents or if you could get by with less than that. Basically for every dependent that you claim, it will exempt $3,500 from your annual salary from taxes. So if you claim 20 exemptions, the payroll program will calculate that your first $70,000 is annual wages is not subject to tax. You also receive an exemption amount for your standard deduction based on whether you are filling out your W-4 as single or married. So just as an example, if your salary is only $50,000 a year, then you certainly could get by with claiming less than 20 dependents.
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