Synonyms for Carry on:

n.

express yourself, render, surrender, offer, manifest, make no secret of something, voice, display, give away, show. baggage check, AIRLINK, baggage allowance, airline, persist, baggage storage, endure, achieve, aerial, air rage, air mile, airfare, persevere, keep going, accompanied baggage. press, engage in, head, flow, walk-on, forge ahead. stay the course, press ahead, follow through, get on, rage, misbehave, raise hell, raise Cain. dally with, date, go together, cheat, cohabit, fool around, go out, court, go with. three-ring circus, maelstrom, muddle, farce, disarray, tumult, rigamarole, chaos, circus, mayhem. carry on (noun)
uphold, continue, proceed, act up, bear on, deal, preserve, conduct, go on.

v.

continue activity (verb)
keep going, persist, endure, achieve, persevere, proceed.
lose control emotionally (verb)
raise Cain, misbehave, act up, rage.
manage operations (verb)
engage in, conduct.
social (verb)
deal, conduct.

Other synonyms:

fool around, dally with, endure, cohabit, misbehave, press ahead. forge ahead. go together, persist, persevere, walk-on. follow through, go with. date, cheat, flow. go out, court. press, get on. head. act up
raise hell.
continue
go with.
misbehave
act up.
persevere
stay the course.
Other relevant words:
raise Cain, persist, engage in, fool around, persevere, forge ahead, head, achieve, conduct, raise hell, court, endure, misbehave, keep going, rage.