Depends on what you mean by "use" your account. Anyone you give your account information (id/password) to could then use your points to order awards for themselves or anyone else. If you are asking about ordering award certificates for persons other than yourself, then the answer is yes. Awards can be ordered for anyone you choose.

If you are asking about having one account for the family and stays by any of your family members have their points credited to that "family" account, then no. Marriott doesn't allow those type of multiple person accounts. Though, when ordering an award, you can combine points from any two accounts to get the needed points for that award.