THESAURUS
predominate
ascendant, be in, be in force, be the rage, be the rule, be the thing, best, bestride, better, cap, control, dictate, dominate, domineer, exceed, excel, go one better, have the ascendancy, improve on, lord it over, master, obtain, outweigh, overbalance, overbear, overbearing, overcome, overpass, overrule, overshadow, overtop, paramount, perfect, play first fiddle, predominant, preponderant, preponderate, prevail, prevalent, regnant, reign, rule, rule the roost, sovereign, surpass, take the lead, top, tower above, tower over, transcend, trump, twist, wear the pants
ROGET THESAURUS
predominate
Superiority
VB
be superior, exceed, excel, transcend, outdo, outbalance, outweigh, outrank, outrival, out-Herod, pass, surpass, get ahead of, over-top, override, overpass, overbalance, overweigh, overmatch, top, o'ertop, cap, beat, cut out, beat hollow, outstrip, eclipse, throw into the shade, take the shine out of, outshine, put one's nose out of joint, have the upper hand, have the whip hand of, have the advantage, turn the scale, kick the beam, play first fiddle, preponderate,
predominate, prevail, precede, take precedence, come first, come to a head, culminate, beat all others, bear the palm, break the record, take the cake, become larger, render larger.
Influence
VB
have influence, be influential, carry weight, weigh, tell, have a hold upon, magnetize, bear upon, gain a footing, work upon, take root, take hold, strike root in, run through, pervade, prevail, dominate,
predominate, out weigh, over weigh, over-ride, over-bear, gain head, rage, be rife, spread like wildfire, have the upper hand, get the upper hand, gain the upper hand, have full play, get full play, gain full play, be recognized, be listened to, make one's voice heard, gain a hearing, play a part, play a leading part, play a leading part in, take the lead, pull the strings, turn the scale, throw one's weight into the scale, set the fashion, lead the dance.