The Controller, after consulting with the Department of Finance, may approve any general plan whereby any state agency which is within a department and which is supported either by a special fund or by a separate appropriation from the General Fund, may make financial adjustments with the department of which it is a part and with any other state agency within the department for services rendered, supplies used, or for a proper proportion of other expenses. A copy of the proposed plan shall be furnished to the Department of Finance before approval by the Controller; and a copy of the approved plan shall be furnished to the Department of Finance.