Synonyms for Get On (same or very similar meaning)
WordNet sense 1 (have smooth relations):
get along with, get along, get on with
WordNet sense 2 (get on board of (trains, buses, ships, aircraft, etc.)):
board
WordNet sense 3 (get on the back of):
bestride, mount, hop on, climb on, jump on, mount up
WordNet sense 4 (appear in a show, on T.V. or radio):
be on
WordNet sense 5 (develop in a positive way):
advance, progress, progress, come on, come along
WordNet sense 6 (grow old or older):
age, maturate, mature, senesce
From the ODE community, based on WordNet
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