Unmarried w/ 2 kids. Live together. Each claims 1 child. If I contribute more, can I file as HOH even though I won't claim both kids?

generally, if you are maintaining a home / household for a qualifying child. relative and you pay at least 1/2  of all expenses for the  home, then you can claim HOH filing status -- the number of qualifying children do not make a difference.  Where it gets sticky , is if each of you take a child and claim HOH  in the same physical home. Can be done? yes  Should it be done ? probably no.  If you do do it, then you have make  very sure that the same home is supporting two households i.e.  funds / expenses are not co-mingled and extremely well documented, if challenged.  It is not an easy path , to live together and keep funds and expenses  completely separate for each household, it is like living in two separate apartments  in the same building.