From Middle English sammen, samnen, from Old English samnian, ġesamnian, from Proto-Germanic *samnōną ("to gather"), from Proto-Indo-European *sem- ("one"). Cognate with Dutch zamelen ("to collect"), German sammeln ("to collect, gather"), Swedish samla ("to gather, collect"), Icelandic samna ("to gather, collect"). More at same.
From Middle English sām ("together"), from Old English samen ("together"), from Proto-Germanic *samanai ("together"), from Proto-Indo-European *sem- ("together, one").
From Middle English sam-, from Old English sām- ("half-; partly; incompletely"), from Proto-Germanic *sēmi- ("half"), from Proto-Indo-European *sēmi- ("half"). Related to semi- (via Latin).