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"with an increasing" is correct and usable in written English.
You can use it to refer to the fact that something is increasing in level, amount, size, etc. For example, "The company's profits have grown steadily with an increasing demand for their products."
Exact(60)
Firstly, we are faced with an increasing complexity of knowledge.
Each model is varied with an increasing amount of detail.
The oil volume fraction increases with an increasing nozzle number.
Meanwhile, Young's modulus diminishes with an increasing temperature.
Morrison, playing with an increasing swagger, soon took control of the match.
Weather may yet intervene, with an increasing chance of rain forecast.
Mr. Mbeki has been credited for handling the crime issue with an increasing sense of urgency.
In many homes, dinner is a flexible concept with an increasing number of variables.
And finally he was taunted, with an increasing sense of confidence, by City's fans.
Plants, animals and ourselves will have to live with an increasing rate of environmental change".
Bitcoin is bought via online exchanges and platforms, with an increasing number of UK options.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com