The City Council today approved a request by at-large Councilor Michelle Wu to begin looking at charging fees for what are now free resident parking permits - and maybe even limiting the number of permits any one family could get.

Wu said the current free-for-all system, in which families can get as many permits as they want, and not be charged a cent, just isn't working. She said there are hundreds of Boston families with five or more permits.

Permit fees would encourage residents who have alternative private spaces to use them, she said. She acknowledged that back when she lived in the South End, she would often park in front of her home, rather than spend the extra 45 seconds to drive out back to where she had a deeded parking space.

By freeing up such spaces, the city could begin to look at such things as visitor passes that residents could provide to guests - which Cambridge has long provided. Currently, visitors to Boston residents in permit-only neighborhoods have to hope one of the few visitor spaces are open.

Permit fees would also raise funds for needed infrastructure improvements, she said.

Councilor Josh Zakim (Back Bay, Fenway, Beacon Hill, Mission Hill) praised Wu as "adventurous and brave" for proposing fee-based permits, but said he fully supports the idea. "It is high time," and any hearings should take an overall look at how Boston is dividing up "its precious curb space" in an age of growing numbers of bike lanes, package deliveries and the like.

Separately, Zakim and at-large Councilor Michael Flaherty proposed a hearing on a new type of parking permit for home health-care workers, who now often have problems finding a place to park without risking a ticket as they visit their patients.