This is known as "paratransit" and it's fairly common, e.g. there's THE RIDE in Boston metro, Wheel-Trans in Toronto, TransHelp in Peel region in the GTA, Handy

This is known as "paratransit" and it's fairly common, e.g. there's THE RIDE in Boston metro, Wheel-Trans in Toronto, TransHelp in Peel region in the GTA, HandyDART in Metro Vancouver... I believe in the US it's a requirement of the ADA for public transit agencies to offer such services. I would imagine here in Canada the legislation is handled provincially, with guidelines for service standards developed by CUTA.