In this [article](https://arxiv.org/abs/2112.01352) (page 2) , the authors say: 

"it is expected, based on known examples, that Calabi–Yau threefolds of large Picard
rank are always elliptically fibered, perhaps after flopping a finite number of curves." 

They did not provide any references for this claim in the paper.
Any supporting examples or references for this claim? 


K3 surfaces of large Picard rank ($\ge 5$) are always elliptically fibered but three dimensional situation is quite different.