In case of multiple insured, we would have to divide the answer into two parts:
1. In case of product with NO U/W question: It is recommend that we have all insured person to sign the application. In case we can obtain only the main insured to sign, the risk is that the un-signed customer can challenge that he/she does not agree to buy insurance coverage and company may have to return the premium, unless we can provide a proof that the un-signed customer know that he/she is buying the policy (regardless of the signing of the application), e.g. call for policy enquiry, accept that he/she buy policy during the confirmation call (if any), make a claim, etc.
2. In case of product with U/W question, we must have all insured to sign the application and answer the U/W question by each individual; otherwise, the company cannot decline the claim and void the policy due to misrepresentation or undisclosed statement.