WordNet sense 1 (continue a certain state, condition, or activity):

continue, keep, proceed, go along

WordNet sense 2 (move forward, also in the metaphorical sense):

advance, progress, progress, pass on, march on, move on

WordNet sense 3 (start running, functioning, or operating):

come on, come up

WordNet sense 4 (continue talking):

carry on

WordNet sense 5 (come to pass):

hap, happen, occur, pass, fall out, pass off, come about, take place