The good news is that you can. The Operation Manual 2 on the Processing of the Members of the Family Class states the following:
What happens if the common-law partner (principal applicant) is married to another person?
“Persons who are married to third parties may be considered common-law partners provided their marriage has broken down and they have lived separate and apart from the spouse for long enough to establish a common-law relationship – at least one year. In this case, they must have cohabited in a conjugal relationship with the common-law partner for at least one year.
Cohabitation with a common-law partner cannot be considered to have started until a physical separation from the spouse has occurred. A common-law relationship cannot be legally established if one or both parties continue their marital relationships.
Officers must be satisfied that a principal applicant is separated from and no longer cohabits with a legal spouse. This evidence may be in the form of a signed formal declaration that the marriage has ended and that the person has entered into a common-law relationship. An officer may require that the person produces other written evidence of a formal separation or of a breakdown of the marriage. Acceptable documents include a separation agreement, a court order in respect of custody of children identifying the fact of the marriage breakdown, documents removing the legally married spouse(s) from insurance policies or will as beneficiaries (a “change of beneficiary” form.)”
In many cases, individuals who are separated from their spouses are not able to obtain a divorce in a timely manner due to different circumstances (court backlogs, missing spouses etc). This policy allows married individuals who are separated and in a common law, relationship to sponsor their current partner.