The phrase "then extends" is grammatically correct and can be used in written English.
It is commonly used to describe a sequence of events or actions. Example: "First, the company will conduct market research, then it will extend its product line to meet the needs of its customers."
Exact(60)
And then extends it some more.
It starts off accommodating your tablet and then extends for groceries (ohyo.me).
Ratliff then extends his investigation, in the second half of the book, to examine Coltrane's legacy.
This cycle then extends to the best students wanting to study with the best faculty".
Colin Stilwell appears to take something out of his pocket and then extends his hand and pulls it back quickly.
"That grub stays in there for two years, eating the cambium and sap wood, then extends down to the roots.
Unfortunately, he then extends his definition to include information passed down by "teaching," a word that raises the same problems as "culture".
The central bank then extends these reserves to the private banking system to set the overnight interest rate at which the banks lend.
Sydney rests on a huge sandstone slab that rises at the harbor cliffs along the Pacific Ocean and then extends scores of miles into the hinterland.
It then extends that PC's display into a viewing application on a second PC over an Ethernet connection or wireless network.
What if a user begins to treat the robot like a slave, and then extends this destructive behavior to a family member or a friend?
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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