"in parallel with this" is correct and usable in written English.
It is used to express something happening at the same time or in the same way as something else. For example, "He continued to work hard at his job, in parallel with this he also began taking evening classes."
Running in parallel with this all-too-familiar tragedy is another story.
Other government initiatives, notably the Big Society policy, will be implemented in parallel with this radical reduction in council spending.
Secondly, and in parallel with this, Washington needs to broker more effective economic and security ties between Seoul and Tokyo.
New factories swelled Vienna's population in parallel with this growth, and the animals found themselves prey to merciless weekend crowds.
I did stay and rebuild the business, but I did it in parallel with this other stuff.
In parallel with this multi-faceted career – Holmes had to slow down after a health scare in 2004 – he remained active in the TA.
"In parallel with this, we will encourage the development of a much bigger independent sector, to supplement the work of the NHS".
Running in parallel with this mission, which doesn't go quite as expected, is an account of what happens thirty years on, when its full implications begin to stir.
"Our concern is that in parallel with this repoliticization of abortion, we have seen an upsurge of anti-abortion activity outside our clinics.
In parallel with this, the wealth gap between the richest and the poorest in Britain has widened consistently since the 1970s.
In parallel with this, the two other men who occupy her thoughts are also strongly contrasted: one, whom she cannot have, the object of physical passion; the other, whom she can, sharing and encouraging her scientific interests.
