When you place a signature field on a form design, the Lock All Fields After Signing option is selected by default. This means all that all form objects will be locked after the field is signed.
If you place more than one signature on the form design, and the Lock All Fields After Signing option is selected for at least one of the signature fields, all form objects, including all signature fields, will be locked after the form is signed.
To ensure that all signature fields can be signed, create a collection of form objects that includes only one of the signature field objects, and make sure that the Lock All Fields After Signing option is selected. After this signature field is signed, all of the objects specified in the collection will be locked. Keep any remaining signature field objects outside of the collection, and deselect the Lock All Fields After Signing option for each one, so that these signature fields can still be signed.
See also 

Considerations for adding multiple signature fields