The Canadian Province of Saskatchewan is the only jurisdiction in the Western World that allows an individual to form a common law marriage while married civilly to another person. It is assumed Saskatchewan also allows civilly married people to remarry without a legal divorce.
No. There would be no common law marriage even if allowed by state law. Generally, in all states of the US and most provinces of Canada, if one party is legally married they cannot establish a common law marriage with another spouse even if common law marriage is recognized by the state. Once a person is legally married they cannot marry again until their marriage is dissolved legally by a divorce.