The phrase "not exclusively because" is correct and usable in written English.
You can use it to indicate that there are multiple reasons for something, and the one mentioned is not the only factor.
Example: "She chose to move to the city not exclusively because of the job opportunities, but also for the vibrant culture."
Alternatives: "not solely due to" or "not only because of".
It all tasted fabulous the last time we were there, partly (but surely not exclusively) because we ate under an umbrella in the garden on a rare 73-degree summer day.
"Not exclusively because of the cold war, but in part also because of national psyche and culture, these two sides are like Ninja masters who have taken up a new profession," he said.
The idea of an individual mandate, he noted in the speech, "has found some favor in the United States Congress, primarily among Republicans, but not exclusively, because it has the appeal of not imposing a business mandate, which has a bad sound to it".
Going back to the bigger picture, the rise in online video watching on TV is not exclusively because people are buying fancier televisions with internet built into them; also playing a role are the consoles that they are attaching to their existing sets.
We now know, mostly but not exclusively because of the recent work of Jonathan Israel (2006, 2001),[7] that the Enlightenment had been from the beginning a complex phenomenon, with a variety of strands crossing it and competing with each other for the achievement of its single purpose of making reason prevail.
It is not exclusively because of those who hold positions of power – it can come from anyone, anywhere, who takes even one step toward building a more sustainable future.
We focus primarily, but not exclusively, on eggs because they are highly nutritious, easy to prepare, can be included in many different dishes, and are a part of a wide range of cultural food menus.
Not exclusively in other mediums because I always love books, but I might try to branch out a little.
Americans fall victim to gun violence not exclusively due to availability, but because the idea of wielding a firearm or having one close by for the most part doesn't really bother us.
That is, people holding negative self-views are preferentially (but not exclusively) drawn to negative feedback because such self-confirming feedback bolsters confidence in the accuracy of negative self-views (i.e., "epistemic" reasons) and serves to avoid the negative consequences resulting from others forming overly positive appraisals (i.e., pragmatic reasons).
– and then I'd have to tell you that Edinburgh doesn't count, because it's not exclusively a comedy festival.
