Can one continue to give monthly charity to several families with the intention of expiating for four previous years of fasting until it is all paid off?

The recipients of expiations (kaffarat) are specifically the poor and the needy. It is not permissible to disburse them to other categories eligible for zakat (definition). The poor person is one who has no wealth or income sufficient for their needs, while the needy person is one who has some wealth or income, but it is not sufficient. It is permissible to give expiation or fidyah (definition) to those whom the giver usually gives charity to, provided they are poor or needy. The obligatory feeding for fasting may be given to a single needy person. However, for expiations specified with a certain number of needy persons (such as ten or sixty needy persons), it is not permissible to give it to a lesser number, according to the majority of scholars, because Allah Almighty commanded feeding a specific number.