The phrase "additional reasons why" is correct and usable in written English.
You can use it when you want to introduce more explanations or justifications for a particular point or argument.
Example: "In addition to the benefits already mentioned, there are additional reasons why adopting this policy would be advantageous for our organization."
Alternatives: "further explanations for" or "more justifications for".
There are additional reasons why a phylogenetic explanation of the obtained pattern is more reasonable.
But these days there are two additional reasons why diplomats are concerned.
UPDATE #2: Prominent originalist legal scholar John McGinnis offers some additional reasons why Trump is likely to be terrible on judicial appointments.
As Mr. Justice DOUGLAS points out in his dissent to the dismissal for mootness in this case, there are additional reasons why this case should not be deemed moot.
Ms. Petrou agreed with me on Friday that this is the current situation, although she also argues that there are additional reasons why big banks have a funding advantage (such as more liquidity in the market for their debt).
Larry Ball discusses additional reasons why foreign-exchange intervention is dropped entirely as a potential tool in later Bernanke speeches; Mr Bernanke may have changed his mind since 2003, but that doesn't mean he's right now and was wrong then.
This is an additional reason why the UK needs to show some atomic atonement – and get on with nuclear disarmament.
There are newspaper articles and interviews, which assert that Twain's life "is an additional reason why the American people should feel grateful".
Guillem will also be dancing with Le Riche in the Paris gala, an additional reason why so many fans have been disappointed not to see the event live and why so many will be watching it online.
An additional reason why Calvi gets my vote over L'Île Rousse is the Bout du Monde, a seafood restaurant on the beach that Mr. Orsini recommended and where I had one of the best meals of my entire journey: an unfussy, superb lobster salad with an inexpensive but delicious dry white wine from Ajaccio.
