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The phrase "and a second case study" is correct and usable in written English.
You can use it when referring to an additional example or analysis in a discussion or report, particularly in academic or research contexts.
Example: "In this paper, we will examine the first case study in detail, and a second case study will be presented to illustrate the broader implications of our findings."
Alternatives: "along with a second case analysis" or "as well as a second case example".
Exact(1)
Additional experiments on datasets filtered to remove members from the same SCOP superfamily and a second case study on Escherichia coli Asparagine Synthetase (PDB id:12as) are reported in the Supplementary Materials (Section S-5.1).
Similar(59)
The limitations of the existing US SRSs that can compromise an efficient and expeditious investigation are exemplified in a second case study of 246 death reports potentially associated with contaminated heparin administration between January 2007 and May 2008 [ 24].
A second case study in the domain of consumer law was carried out with Italian corpora.
As a second case study, we conjugated linker 1 to the adhesion peptide cRGD to yield cRGD-NO2 (Fig. 3a).
In a second case study we simulate the LSS dynamics of a Mars mission scenario.
A second case study examines the evolution of products over the years.
So Stelios is launching a second case study at a busy Burger King on Piccadilly Circus.
In a second case study, the gene ADD2, encoding the adducing 2 isoform a, was analyzed.
We conducted a second case study using data from the United Kingdom [see Supplemental Material, Table S3 (doi:10.1289/ehp.0900648.S1)].
In a first case study, the plasma and the tissue reached equilibrium very quickly.
In a third case study, a brand-new green living complex was built, and residents were surveyed before and after they moved in.
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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