Whenever the county treasurer has furnished a bond by personal sureties or by a surety company, the board of county commissioners may require the treasurer to give an additional bond, or additional sureties if, in the opinion of a majority of the commissioners, the existing security shall have become insufficient. The board may demand and receive from the county treasurer an additional bond, with good and sufficient security, in such sum as it may direct, whenever, in its opinion, more money shall have passed or is about to pass into the hands of the treasurer than is covered by the penalty in the previous bond. The giving of an additional bond or of additional sureties on an existing bond shall not invalidate any previous bond or bonds, nor discharge the sureties from any liability thereon.