Yes, domestic partnerships.
All government employees are protected by the U.S. Constitution against irrational discrimination based on sexual orientation or gender identity. In addition, some measure of protection already exists under Title VII based on gender, which has been held to include gender identity and expression.
The U.S. Equal Employment Opportunity Commission (EEOC) and several courts have interpreted Title VII to protect transgender employees, and the EEOC has interpreted Title VII to cover sexual orientation discrimination. The Supreme Court has held that the EEOC's interpretations of Title VII are entitled to "great deference."
The Maine statute specifies only an unmarried person or married couple may jointly adopt. See 18-A Maine Statutes 9-301. In a lower court case, however, involving a same-sex couple seeking to jointly adopt, the Court concluded that "section 9-301 does not prohibit a joint adoption petition by two unmarried persons." See In re M.A., 2007 ME 123 (2007).
Not expressly permitted by statute, but see In re M.A., 2007 ME 123. State is fairly tolerant.