Such a change would have to be negotiated with the union that represents principals, which has strongly resisted the idea.
The evaluation systems required agreements between administrators and the unions representing teachers and principals in each of the districts.
Statewide education associations representing teachers, principals and superintendents all opposed the Republican move.
All the responsible parties - top board officials and unions representing teachers, principals and custodians - say they are horrified by such cases.
Some officials saw this as another swipe at the union, since it has long been the only body representing principals in policy discussions.
The fight over the appointments drew unusual interest from unions representing teachers and principals.
The union that represents New York's principals and assistant principals already has expressed its opposition to his approach.
But the union representing principals lashed out at his plan, saying it was unfair for him to set a target before carefully evaluating everyone.
Labor unions representing principals and teachers have long criticized what they say is heavy-handed, top-down management by the Bloomberg administration.
But devising an evaluation system agreeable to unions representing teachers and principals in more than 700 school districts has presented a challenge.