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The phrase "subsequently built on" is correct and usable in written English.
It is typically used when talking about something that was added or expanded upon at a later point in time. Example: "The foundation for the company's success was laid by its founder, and it was subsequently built on by generations of dedicated employees."
Exact(8)
In a few locations, uranium tailings have been used for landfills and were subsequently built on, resulting in possible increased exposure to radon.
The "New Town" that was subsequently built on the site was planned as an industrial-residential complex.
The original wooden building was relocated in 1864, and the new church subsequently built on its site.
It survived until the dissolution of the monasteries in 1539, and a house was subsequently built on the site.
A medieval church was subsequently built on the site, during the 19th-century demolition of which Norman capitals were found in the masonry of its tower.
The Fatimids subsequently built on their victory over Atsiz and besieged Damascus in 1077 and again in 1078, but both attempts to take the city were unsuccessful.
Similar(52)
The alternative is to spread awareness of clinical audit and to use the methodology locally at departmental level, and subsequently build on this to form a national system.
To better support the utility of this new technique we will describe the density k-NN (dk-NN) approach proposed by Sahigara et al. [12], which was the basis from which we developed the herein proposed method; we will subsequently build on this explanation to transition into the RDN algorithm.
Each year subsequently builds on previous year's work through a spiral approach to learning [ 18].
We subsequently build on these results to examine what happens when individual elements may be highly diffusible.
Indeed scientific progress depends on the ability of researchers to access and exploit data and materials reported in publications so that they can subsequently build on these findings.
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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