Synonyms for Move on:

n.

convert, renounce, capitulate, revise, backpedal, see reason/sense, change your mind, adapt, move with the times. treasure, thrive on, rejoice, jump for joy, look forward to, live happily ever after, brighten, rejoice in, cheer, be happy for someone. post, send, parachute, farm out, relocate, pack off, bundle off, route, dispatch, ship. sample, change direction/course, change over, break with, strike out, turn your hand to something, begin, give something a try, branch out, try your hand at something. move on (noun)
march on, go on, advance, progress, pass on.

v.

advance (verb)
progress, dispatch.
proceed (verb)
travel.
progress (verb)
keep going.

Other synonyms:

abandon. depart
get away.
progress
keep going.