The phrase "in process of acquiring" is correct and can be used in written English.
It means that something is currently being obtained or gained. You can use it when describing a situation where someone or something is actively working towards obtaining or gaining something. Example: The company is currently in the process of acquiring a smaller rival in order to expand their market share.
Exact(3)
It is, however, in process of acquiring cross-border transfer service MoneyGram for $1.2 billion, after seemingly winning a fierce bidding war.
Environment taxation policy in most of the developing nations is still in infant stage and it is in process of acquiring a laudable shape.
Alibaba itself operates a range of affiliates, including $60 billion valued Ant Financial — which it is in process of acquiring one-third of — and a logistics unit called Cainaio.
Similar(57)
The compact cars, midsize cars and what Toyota officials described as minivehicles are all to be produced in Tianjin, where F.A.W. is in the process of acquiring a controlling stake in a local car maker.
Although participating ICUs in Peru are in the process of acquiring the necessary infrastructure for electronic medical records, none currently have it in place.
Shares in AOL, which is in the process of acquiring the American multi-media business Time Warner, reached a peak of more than $95 at the end of last year but were trading yesterday at $65, having climbed 4%.
The five models tested showed three major categories of deficit: in the process of acquiring the CR, in the amplitude of the CR, and in the timing of the CR.
While AOL (which owns TechCrunch) is in the process of acquiring Yahoo, over in Malaysia a similar consolidation was announced this week — although not quite on the scale of AOL-Yahoo (Oath?!) and its $4.48 billion price tag.
Critically, habituation phenomena can be studied with passive paradigms, which have tremendous advantages in the study of speech perception, particularly for the study of populations in the process of acquiring language, or adult populations differing in their early language experience.
Apple and Motorola - which Google Inc is in the process of acquiring - are engaged in global patent litigation, part of a broader legal fight over the smartphone market, with billions of dollars at stake.
There is more: Finnish telecommunications equipment company Nokia is in the process of acquiring 2007 Fast Tech member Navteq in an $8.1 billion takeover deal.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com