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This is strictly my opinion. You should check with a CPA or other tax authority for a definitive answer.
That said... I don't think there is a maximum number of allowances. The W4 is a guideline that your employer uses to figure
out your income tax withholding. If you claim too many allowances, your employer will not take out enough taxes, and you'll
have to pay them in April. If you claim too few allowances, your employer will keep back more income tax, and you are more
likely to get a refund in April.
The main problem to taking a lot of allowances is the risk of additional penalties. The IRS requires you to pay a certain
percentage of your total tax over the course of the year. If you don't do so, they will add penalties to your final tax bill.
Some people claim zero allowances, therefore having the maximum tax withheld, but still it's not enough (usually these people
have investment or non-wage income). They have to pay estimated taxes every quarter in order to avoid the penalties.
To avoid trouble and unexpected tax bills while still maximizing the use of your earnings, you should aim to claim enough
allowances so you pay or are refunded a small amount at tax time. You can adjust your allowances at any time, so use this
year's tax return to determine whether to take more allowances (you got a large refund) or take fewer (you had to pay a large
tax balance). Take unusual events into account too, like the purchase/sale of a house, birth or emancipation of a child, job
change, bonuses, etc.
If you have 28 kids then you can take that many exemptions and more. There is also a worksheet that lets you calculate how
much you plan to deduct for itemized deductions, and then estimates the additional amount of exemptions you can take.
Example of another Article
There is no stated maximum, but you should be careful with how many you claim. If you claim too many, then you may have too
little taken out of your paycheck, and then you will owe money come tax time. If you owe too much money, the IRS may force
you to pay next year's income tax ahead of time in quarterly installments, and that is a real pain. That is attention you do
not want.