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The phrase "a second possibility exists" is correct and usable in written English.
You can use it when discussing options or alternatives in a situation, particularly when presenting multiple choices or scenarios.
Example: "While the first option is viable, a second possibility exists that may yield better results."
Alternatives: "Another option is available" or "An alternative exists."
Exact(2)
A second possibility exists: that unlike WT cells, the mutant crypt cells fail to withdraw from the cell cycle to repair lethal damage.
A second possibility exists in that ATMIN regulates not only Dynll1 expression, but also expression of other loci; we have demonstrated downregulation of Ift88, Ift172, Ift140 and FoxJ1.
Similar(58)
However, a third possibility exists that Psn regulates CBP through a mechanism that is currently unknown.
Finally, a third possibility exists: Gli3 processing and Gli2 inhibition could be sensitive to different levels of PKA activity.
However, if we consider these three types of attitudes from another angle, viz. the interaction between the embedding attitude verbs and the embedded epistemic modals, we may ask whether a fourth typological possibility exists, as Table 1 shows: could there be a fourth class of attitude verbs, which allows epistemic necessity but not possibility modals in their complement clauses?
A second possibility is biological.
A second possibility is and so that.
This approach exemplifies the widely accepted Euclidean reductio ad absurdum, for which a proposition that cannot be demonstrated as true proves that its contrary is instead true, since a third possibility does not exist (tertium non datur).
First, the possibility exists that incomplete, defective genomes are integrated in the vector particles [ 25].
Third, the possibility exists that, even if many of the observed interactions are functionally important and, by inference, the respective binding sites are subject to purifying selection, the binding sites for different partners tend to overlap such that the number of amino residues in these sites increases only slowly with the increase in the numbers of interactions.
Rationally, this decision should be based mainly on clinical judgment, and a biopsy considered, if its results would affect clinical decision making, or if a possibility exists of unrelated disease (second primary tumor or benign lesion).
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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