I researched all 40 something Blue Plans in the US.
Blue Cross of Kansas City is for profit as a result of a lawsuit alleging they had overstepped what a nonprofit is allowed to do.
Health Care Service Corp (Blue Cross IL, NM, OK, TX) is for-profit.
Anthem (Blue Cross part CA, CO, CT, IN, KY, ME, MO, NV, NH, OH, part VA, WI), is for profit publically traded.
AL, AZ, AK, part CA, FL, HI, ID, KA, LA, MA, MI, MN, MS, MT, NE, NJ, Excellus (central NY), Northeast NY, NC, ND, Northeast PA, Southeast PA, Central PA, RI, SC, TN, VT, WY, Carefirst (DC, MA, part VA), Highmark (part PA, DE, WV), Premera (AK, WA), Regence (ID, OR, UT, WA), and Wellmark (IA, SD) are all nonprofit. Carefirst and Regence attempted to go to for-profit at one time but did not due so.