progressively sociable

Refers to an "incrementally moving up the scale" degree of "closeness" --- i.e., gently 'n' gradually narrowing the "aura" of personal space --- between yourself and someone else, till you've eventually proceeded from merely sitting across from the person all the way up to being either tightly wrapped around him or bodily plastered overtop of him on the bed/couch or on the grass in your back yard.

My neighbor's furry black Lab realized that I was getting bored and lonesome while I was sitting in the front yard to wait for his master to get home, and so he sympathetically performed the classic friendly-canine "progressively sociable" routine on me --- first sitting at my feet and letting me smooth his forehead and riffle his fluffy ears, then scooching forward a bit and placing his front paws on my shoe-lacings, then gently nudging my chest backwards with his head so that he could move his paws up onto my shins, then easing on up even closer to me so that I'd slide my legs down flat and he could rest his paws on my kneecaps, then moving up further to place his paws on my hips, then again using his head to softly lean me even further back, and so on --- till he had me totally lying flat on my back and he had fully stretched out and settled himself on top of me. Kinda weird --- not to mention heavy --- having a huge fuzzy 90-pound dog resting peaceably on top of me, but I realized he meant well, and that he was merely trying to ensure that I didn't feel quite so lonely from waiting till his master got back.