Can human service corporations care for the poor and multi-problem clients while continuing to generate profits? what ethical issues are involved?

Yes, with Profit-making firms. Private non-governmental entities that differ from the traditional private voluntary agencies. Corporate social welfare benefits help stabilize prices and maintain economic growth. Social welfare policies also relieve the social and economic dislocations caused by the uneven nature of economic development under capitalism.
 

Government social pro-grams erode the work ethic by supporting those not in the labor force. Second, because they are funded by taxes, public sector social welfare programs divert money that could otherwise be invested in the private sector.

People care deep about "organizational justice" and perform better when they believe that their workplace is treating them with respect and ensuring them rights and equitable reward structures. Organizations make their ethical priorities evident in multiple ways, including through policy; the criteria for hiring, promotion, and compensation; and the fairness with which they treat their employees.