Can two people in the same household claim head of household?

Yes it is possible. IRS considers a household not to be limited to residents in a structures ("by that logic there would only be one head of household for an apartment complex 'if it were one address'"), instead they choose to understand that more than one household can reside in the same building with the same address at the same time. Beware there are rules for establishing more than one household at the same address.