The phrase "a third explanation is" is correct and usable in written English.
You can use it when introducing an additional reason or rationale in a discussion or argument.
Example: "After considering the first two explanations, a third explanation is that external factors may have influenced the outcome."
Alternatives: "another explanation is" or "a further explanation is".
But a third explanation is that the strongest teams simply got lucky.
A third explanation is that Mr. Hayami is on a personal mission to force a restructuring of the Japanese corporate and financial structure.
A third explanation is that Obama's tweets benefit from spite-kindness: his supporters are keen to make a point to their opponents.
A third explanation is that we as parents have made our children so anxious they (like mine) routinely and fastidiously check themselves.
A third explanation is that the origin of therapsids occurred in a different geographic area, one that either does not preserve rocks with fossils from this time or has a fossil record that has not been thoroughly studied.
Perhaps neither: a third explanation is that countries with a big share of foreign prisoners tend to be those with low overall levels of imprisonment so it may be more accurate to say that Britain locks up a lot of natives than to assert that it imprisons few foreigners.Either way, immigration means that the police need more money, like any other public service.
A third explanation was that highly educated women were benefiting from advances in "assisted reproductive technology" that enable them to spend more years at university without reducing their chances of future parenthood.
A second explanation is the old political-bureaucratic imperative.
A second explanation is more relevant to the work onstage.
A second explanation is that Islam bans usury.
A second explanation is that "Caritas in Veritate" is the work of many hands.
