I have a permit that will expire on Monday. I wanted to renew or extend it. Can it be renewed on the day it expires?

That's all up to your local chief of police, better contact them quickly.

More often than not they will only sign the extension at expiration or after they expire.  But it's all over the map

More often than not they will only sign the extension at expiration or after they expire.  But it's all over the map

Yup, all over the map.  My town extended mine for the full maximum 180 days when I first picked them up!

In saddle brook they'll extend it with no problem. I've had to do it more then once.