Yes, you can do that. You can split the children anyway you want.
But, as others have explained, it almost never works out to your advantage. But the only way to be absolutely sure is to to do trial returns. This tool can be helpful, in doing that: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1
If you want to see something appalling; try trial returns for if you weren't married, but just living together. Again, you can split the kids any way you want. The higher earning parent can file as Head of Household (as long as he claims at least one child). The other parent files as Single.
