Often,we just walk around the town center,seeing as many our

"seeing as many our friends as we can"是做主句“we just walk around the town center”中主语“we”的伴随状语.
此种情况的发生是由于主句中已存在一个充当谓语的动词“walk”,在非复合句（如宾语从等）中,一句话中只可出现一个谓语动词,故要再出现一个动词必将它改成状语.
并且,可以看到,"see"后面加的是"ing"而非改成它的过去分词"seen"就是因为"seeing as many our friends as we can"与主句主语的关系是主动关系.
P.S.非复合句（如宾语从等）中,一句话中只可出现一个谓语动词,故要再出现一个动词必将它改成状语.这时,如果这个动词与主句主语为主动关系,则改成动词的现在分词形式；如为被动关系,则改为动词的过去分词形式.