In connection with any such petition, the authority of the department is limited to the granting of such stays as are necessary for it to complete its investigation and make its findings and, if it makes such findings, to the granting of an order permanently staying the imposition of the entire suspension or of that portion of the suspension not otherwise conditionally stayed by the decision of the department. If the suspension was imposed as a result of an accusation filed by another public officer acting in his official capacity, the department shall not order such permanent stay of suspension without the written concurrence of such other public officer.