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"is extended with" is correct and usable in written English.
You can use it to indicate the addition of something onto something else. For example, "The store's sale period is extended with an additional 10% discount on all items."
Exact(60)
The main contributions with respect to this extended version are the following: The initial proposed formalism is extended with two new modalities for expressing permissions and system obligations.
This model is extended with parametric uncertainties.
In Sanskrit the ending is extended with -a: martyāy-a.
The doubling theory is extended with a new approach.
The second one is extended with the thermal diffusion.
Our automated test suite is extended with every release, but bugs always slip through.
A recently developed non-linear control design based on feedback linearization is extended with integral action.
To process non-text submissions, the system is extended with the appropriate converter.
An existing non-linear control design based on feedback linearization is extended with integral action.
In the next step PROFInet V3 is extended with capabilities for high sophisticated motion control application.
The identification scheme is extended with a proposed algorithm for the model order selection.
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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