You really can. To qualify for the Parent Plus loans you just have to meet the minimum standard of not having defaulted on any prior government loans, not have declared bankruptcy and not be more than 90 days behind on any major debts. Most people can meet these requirements. Year after year, kid after kid.
It is not a good idea, but many people, including the former governors of Maryland and Indiana (now VP) borrowed this way for multiple kids to go to college.