How many exemptions on tax returns can be filed?

That depends.

Taxpayers in the United States are allowed one tax exemption for each person they can qualify as a dependent on their tax return. They may also claim a personal exemption for themselves and for a spouse if the spouse qualifies as a dependent. Theoretically a taxpayer can file for as many exemptions as can be qualified; however the alternative minimum tax may be enforced if the IRS finds a large number of exemptions or other deductions.