go on to

go on to (something)

To progress to something better or more prominent. Quite a few soap actors have gone on to win or be nominated for Oscars, actually. After being an intern there for three years, I'm ready to go on to bigger and better things. Did that famous child actor go on to do much as an adult?
See also: go, on

go on to something

to advance to something or to doing something. After a few years she went on to even greater heights. Larry went on to found his own company.
See also: go, on
References in classic literature ?
As to which quantity there was a perpetual fight going on between the master and his form--the latter insisting, and enforcing by passive resistance, that it was the prescribed quantity of Homer for a shell lesson; the former, that there was no fixed quantity, but that they must always be ready to go on to fifty or sixty lines if there were time within the hour.