"go on existing" is correct and usable in written English.
You could use it to emphasize the continuation of something, or the fact that something will continue to exist. For example, "London will go on existing long after I am gone."
Nobody, perhaps out of kindness, queried the premise of the motion – to ask if "Corbyn's Labour" exists or will go on existing.
He said: "A visit to Yad Vashem, the Holocaust Museum in Jerusalem, will convince you why the state of Israel exists and must go on existing.
The most enjoyable works of fiction present us with convincing worlds; we believe our favourite characters existed before "once upon a time" and go on existing after the final full stop.
One of the immigrant narrators of "Nowhere Man" has the feeling that "most of the things in this world would go on existing whether I lived or died.
If, having obtained that, she allows the capacity for pleasure to go on existing, she does so only out of absentmindedness, just as certain insects go on wearing their mating colors after the mating season is over.
And the gravelly beach and the rough boat deck where they meet in her dreams are "like a place that will go on existing whether you are there or not, and that in fact is still there".
So it would seem that Socrates cannot be identical with grumpy Socrates after all, because in these other possible worlds, while Socrates goes on existing, grumpy Socrates does not exist or so one might think.
One Cecily Crocker became Cecily Eaves and had a gay son who wrote stories and poems; another went on existing in her imagination, and quite possibly didn't pass her 11-plus, or, when mocked by a pompous headmistress for her "awful Cockney accent", instead of growing quietly determined, left school at 15.
John Bassett, now at RUSI and formerly GCHQ's Senior UK Liaison Officer in Washington, adds that much of the new government funding has gone on, "existing programmes... designed to get a really strong grip on global situational awareness".
From this position, the article puts forward a theory on the role of ecological catastrophe narratives in current popular culture, before going on to review existing critical work on ecologically-charged popular films and novels which attempts to assess their effects on their audiences.
Founders may have better luck with funds early on in their investment cycle, when the VCs have more capital, and when they have less going on with their existing portfolio of companies and other deals.
