Other mods to consider, depending on the assault rifle in question, include Heavy Caliber (this kills your accuracy though), Hunter Munitions, basic elemental mods (those that give +90% damage), and really just about anything else that increases damage, crit, status, or multishot significantly. Most high tier assault rifles are good for both crit and status so you'll be using a lot of these mods on the same weapon. a high fire rate with at least a ~15% base status chance) then you want dual stat mods (those that give +60% status chance and +60% elemental.
a base crit chance of ~20% with a 2x multiplier or thereabouts), then you want crit mods like Vital Sense and Point Strike.
As for other mods, it depends on the assault rifle. First and foremost, you want Serration and Split Chamber on pretty much every primary weapon without question.