"alongside doing" is correct and usable in written English.
You can use it when talking about two or more activities happening at the same time. For example, "I'm studying for my final exams alongside doing my part-time job."
At first, she was merely giving bread away in the playground, alongside doing cleaning and book-keeping jobs, but gradually bread took over.
As the group marched towards the science quad, Tom Holder, the energetic young British activist who played an active role in the Pro-Test movement at the University of Oxford, ran alongside doing his best to get some chants started.
And a crisp chenin blanc alongside does a lot for it, too.
Two board-certified dermatologists who were tested alongside did worse: they got the answer correct sixty-six per cent of the time.
"I'm kind of tired of posing for pictures, I'm tired of putting my thumb up when the guy alongside does.
This is one of the better cross-genre collaborations we've seen lately (alongside "Do Ya Thing").
There will also be a four square (the actual schoolyard game) court they're doing alongside Pepsi.
You have an Assembly Member who works alongside you doing that part of the work in Cardiff," he said.
They've been campaigning alongside us, doing posters, asking people to sign the petition – they've handed the petition to Barnet council.
"Many nurses now find themselves in a position where they're working alongside someone doing the same work but earning vastly different sums," she said.
The closest translation we have is "killing time". But "il dolce far niente" demands more: to intentionally let go and prioritize being alongside of doing.
