"Close companionship" refers to a deep and strong relationship between two or more individuals. It implies that they are very close, bonded, and spend a lot of time together, supporting and caring for each other. Full definition
When we respect our bunny for what it is and behave accordingly, we can look forward to many years of close companionship with one of the world's most fascinating and cute creatures. (smallanimalchanel.com)
Because it brings him into close companionship with you and you'll be happy too because you and your dog have found a means of communication. (findme4info.com)
Today, we often refer to these outdoor cats, who don't always rely on or seek close companionship with people, as feral or community cats. (alleycat.org)