Starting Saturday, it will investigate hosts who control multiple listings and will jettison “unwelcome commercial operators” — people running illegal hotels in private homes. “We want to continually evolve the platform so it serves the best interest of each city we’re in,” said Chris Lehane, the former Clinton White House spin doctor and “master of disaster” who is now Airbnb’s head of global public policy. The numbers show that 1,149 listings, or a fifth of all full-home rentals here, are controlled by hosts who rent more than one entire home via the site. Since local law restricts vacation rentals to permanent residents offering their own home, listing multiple properties is a red flag. The company’s latest move comes after years of criticism by activists who say lucrative vacation rentals gobble up some of the city’s precious housing stock. […] that same election added Airbnb critic Aaron Peskin to the Board of Supervisors, creating a new progressive majority that appears poised to weigh more-restrictive laws for short-term rentals. Investigating suspected violators is difficult — so much so that officials pleaded with Airbnb and other vacation-rental sites in January for help weeding out bad players. Since all rentals are booked and paid for via Airbnb’s site, it could easily highlight those that flout San Francisco’s three-month cap on rentals of entire homes. […] it said that single homes in San Francisco were rented a median of 48 nights a year and emphasized that “the vast majority” of local hosts appear to be renting their homes only occasionally. The company said it will launch twice-monthly email blasts encouraging hosts to register, on top of previous town halls, social media advertising and email campaigns. Last month, the city told registered hosts that they must itemize and pay tax on all the furniture, sheets, blankets, pots and pans used in their rentals, and offered an 83-page manual on how to do so.