The mayors of Oakland, Sacramento and more than a dozen other California municipalities are joining San Jose in a campaign to buy out the investor-owned PG&E Corp. and turn it into a giant customer-owned cooperative.

The idea, first floated last month by San Jose Mayor Sam Liccardo, is winning support from mayors and county officials who represent nearly one-third of the population served by PG&E’s utility subsidiary, Pacific Gas & Electric Co.

The...