walk with someone
to walk in the company of someone. Why don't you walk with me for a while? Can I walk with you?
walk with something
1. to walk with the aid of something, such as a cane, crutches, etc. You can recognize her easily. She walks with a cane. Dan walks with the help of a crutch.
2. to walk in a characteristic manner, such as with a limp, halting gait, a sprightly step, etc. Martha's uncle walks with a limp. I have always walked with a halting gait.