No - The current procedure allows a resident to have one permit per car per house which is seen as a fair and consistent approach which gives all residents a reasonable chance of finding a parking space.
The Council gets many requests for permits however, if the resident has a personal car and a company car for instance, they would have to choose which car to use the permit on. I am sure that you can appreciate that if we gave a resident 2 or more permits then parking spaces would be rapidly taken up which other residents could make use of, which would not be an overall fair approach.