No, two people in the same household cannot both claim HOH - only one person can pay *more* than half.

Does your BF have a related dependent (usually a child) to qualify for HOH?  See below.

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You may be able to file as head of household if you meet all the following requirements.

1. You are unmarried or “considered unmarried” on the last day of the year.
(You could be considered unmarried if your spouse did not live in your home at any time during the last 6 months of the tax year).
If you were considered married for part of the year and lived in a community property state, special rules may apply in determining your income and expenses. See Publication 555 for more information.

2. You paid more than half the cost of keeping up a home for the year.

3. A “qualifying person” lived with you in the home for more than half the year (except for temporary absences such as school) - a parent does not have to live with you to be a qualifying person.

4. If the qualifying person is your qualifying relative, their gross income must have been less than $4,050 (do not include non taxable Social Security) and you provided more than 1/2 of their support

5. You must be able to claim the exemption for the qualifying person except in the case of divorced or separated parents (that lived apart) and the noncustodial parent is claiming the exemption.

A Qualifying person is either:
A qualifying child or a qualifying closely related relative and meets certain other requirements, however if you are considered unmarried it can only be your child, stepchild, or foster child.

See IRS Publication 17 for more information about who is a qualifying person and a worksheet to determine the cost of keeping up a home.

See IRS Pub 17 for more information

https://www.irs.gov/publications/p17/ch02.html#en_US_2016_publink1000170792