Our company practices segregation of duties - three signatures are required for every payment of contract. One to approve the spending (budget), one to approve the contract, and one to approve payment. So to contract signing, minimum of two is required. For payment, three.
These are minimum number of signatures, and our company requires anyone between the purchasing/contracting officer and the signatory signs for recommendation.
I would like to add another point - less authority amount shall be given for change order amount. Our company has a separate authority for signing change orders which is approximately 10%. Mind you, this is an aggregate change order amount so it is likely that the highest level sees and approves change orders.