The security required under this part shall be cash or securities permissible under state law as security for deposit of state funds and in such amount as the department may require but in no case in excess of the limits specified in Section 24350 in reference to the limits of a policy or bond. If at the time of the accident there is in effect a liability policy or a bond meeting the requisites of this part other than in the amount of coverage set forth in Section 24350, the department may consider such policy or bond in fixing the amount of security. The person depositing security shall specify in writing the person or persons on whose behalf the deposit is made and, at any time while such deposit is in the custody of the state agency with which the deposit is made the person depositing it may, upon approval of the department, amend in writing the specification of the person or persons on whose behalf the deposit is made to include an additional person or persons; provided, however, that a single deposit of security shall be applicable only on behalf of persons required to furnish security because of the same accident.